The Unit Circle
The Building Block to Calculus
Brett Herschel
EDCI 270
Navigation
• To move forward, use
• To move backward, use
• To go to the angle review, use
• To go to the radian review, use
Students
• 9th – 10th grade
• Trigonometry Students
• Middle Class Community
• Little or no prior knowledge
• Teacher will assist students if any
problems occur
Objectives
• Given the presented slides on the Unit Circle,
students will need to memorize both the Radian
and Angle values with 100% accuracy
• Given an assessment of the Unit Circle, students
will need to answer the questions with 100%
accuracy
Learning Environment
•
•
•
•
Classroom setting
Computer station
May work alone, or with one partner
Students will read through lesson, do the quiz,
and show the teacher when they are finished
Introduction to the Unit Circle
Today we will learn about the importance of the
Unit Circle. Here is a short video on the
importance of the Unit Circle.
The Unit Circle
First, we will discuss the angle values
for the Unit Circle, and their
corresponding points
Sin(θ) = y-value
Cos(θ) = x-value
Students may use a calculator to solve
the homework problems, but they will
need to memorize values for quiz
The Unit Circle
A simple way to memorize the Unit
Circle is to learn all of the angle
values for the First Quadrant. The
points in the First Quadrant will
correspond with the points in the
other 3 Quadrants, with the
exception of knowing whether the
value is positive or negative
The Unit Circle
• 0◦
• 210◦
•30◦
•225◦
•45◦
•240◦
•60◦
•270◦
•90◦
•300◦
•120◦
•315◦
•135◦
•330◦
•150◦
•360◦
•180◦
The Unit Circle
Sin(0◦) = 0
Cos(0◦) = 1
The Unit Circle
Sin(30◦) = ½
Cos(30◦) = √3/2
The Unit Circle
Sin(45◦) = √2/2
Cos(45◦) = √2/2
The Unit Circle
Sin(60◦) = √3/2
Cos(60◦) = ½
The Unit Circle
Sin(90◦) = 1
Cos(90◦) = 0
The Unit Circle
Sin(120◦) = √3/2
Cos(120◦) = -1/2
The Unit Circle
Sin(135◦) = √2/2
Cos(135◦) = -√2/2
The Unit Circle
Sin(150◦) = 1/2
Cos(150◦) = -√3/2
The Unit Circle
Sin(180◦) = 0
Cos(180◦) =-1
The Unit Circle
Sin(210◦) = -1/2
Cos(210◦) = -√3/2
The Unit Circle
Sin(225◦) = -√2/2
Cos(225◦) = -√2/2
The Unit Circle
Sin(240◦) = -√3/2
Cos(240◦) = -1/2
The Unit Circle
Sin(270◦) = -1
Cos(270◦) = 0
The Unit Circle
Sin(300◦) = -√3/2
Cos(300◦) = 1/2
The Unit Circle
Sin(315◦) = -√2/2
Cos(315◦) = √2/2
The Unit Circle
Sin(330◦) = -1/2
Cos(330◦) = √3/2
The Unit Circle
Sin(360◦) = 0
Cos(360◦) = 1
The Unit Circle
• Before we move on, here are a few practice
questions to see what you know
The Sin(180◦) is?
A. 1
B. 0
C. 1/2
The Unit Circle
Correct!
The Sin(180◦) is 0. Good Job!
The Unit Circle
Incorrect.
Remember that the Sin(180◦) is a corresponding
point to the Sin(0◦), which is 0.
The Unit Circle
What is the Cos(225◦)?
A. -√2/2
B. √2/2
C. 1/2
The Unit Circle
Correct!
The Cos(225◦) is -√2/2. Good Job!
The Unit Circle
Incorrect.
Remember that the Cos(225◦) is a corresponding
point to the Cos(45◦), which is √2/2. But
Cos(225◦) is on the negative side of the Unit
Circle, so the answer is -√2/2.
The Unit Circle
Next, we will discuss the Radian
values for the Unit Circle, and their
corresponding points
Sin(θπ) = y-value
Cos(θπ) = x-value
Students may use a calculator to solve
the homework problems, but they will
need to memorize values for quiz
The Unit Circle
Like the angle values, a simple way to
memorize the Unit Circle is to learn
all of the radian values for the First
Quadrant. The points in the First
Quadrant will correspond with the
points in the other 3 Quadrants, with
the exception of knowing whether the
value is positive or negative.
The Unit Circle
•0
• 7π/6
•π/6
•5π/4
•π/4
•4π/3
•π/3
•3π/2
•π/2
•5π/3
•2π/3
•7π/4
•3π/4
•11π/6
•5π/6
•2π
•π
The Unit Circle
Sin(0) = 0
Cos(0) = 1
The Unit Circle
Sin(π/6) = ½
Cos(π/6) = √3/2
The Unit Circle
Sin(π/4) = √2/2
Cos(π/4) = √2/2
The Unit Circle
Sin(π/3) = √3/2
Cos(π/3) = ½
The Unit Circle
Sin(π/2) = 1
Cos(π/2) = 0
The Unit Circle
Sin(2π/3) = √3/2
Cos(2π/3) = -1/2
The Unit Circle
Sin(3π/4) = √2/2
Cos(3π/4) = -√2/2
The Unit Circle
Sin(5π/6) = 1/2
Cos(5π/6) = -√3/2
The Unit Circle
Sin(π) = 0
Cos(π) =-1
The Unit Circle
Sin(7π/6) = -1/2
Cos(7π/6) = -√3/2
The Unit Circle
Sin(5π/4) = -√2/2
Cos(5π/4) = -√2/2
The Unit Circle
Sin(4π/3) = -√3/2
Cos(4π/3) = -1/2
The Unit Circle
Sin(3π/2) = -1
Cos(3π/2) = 0
The Unit Circle
Sin(5π/3) = -√3/2
Cos(5π/3) = 1/2
The Unit Circle
Sin(7π/4) = -√2/2
Cos(7π/4) = √2/2
The Unit Circle
Sin(11π/6) = -1/2
Cos(11π/6) = √3/2
The Unit Circle
Sin(2π) = 0
Cos(2π) = 1
The Unit Circle
• Before we move on, here are a few practice
questions to see what you know
The Sin(5π/6) is?
A. 1
B. 0
C. 1/2
The Unit Circle
Correct!
The Sin(5π/6) is 1/2. Good Job!
The Unit Circle
Incorrect.
Remember that the Sin(5π/6) is a corresponding
point to the Sin(π/6), which is 1/2.
The Unit Circle
What is the Cos(7π/4)?
A. -√2/2
B. √2/2
C. 1/2
The Unit Circle
Correct!
The Cos(7π/4) is √2/2. Good Job!
The Unit Circle
Incorrect.
Remember that the Cos(7π/4) is a corresponding
point to the Cos(π/4), which is √2/2.
The Unit Circle
Once students are comfortable that they know the
information they may move on to the Quiz. If the
students still feel that they need to review, they
may hit the review buttons at the bottom of the
screen.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
The Unit Circle: Quiz
Quiz Directions: Students will now take a quiz
testing their knowledge of the Unit Circle. The
quiz is multiple choice and students will need to
score an 80% percent or better to pass the
assignment. Good luck!!
The Unit Circle: Quiz
Question 1
• What is the Sin(π/4)?
A. 1/2
B. -√3/2
C. √2/2
D. -1/2
Correct!
Please go on to Question 2.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 1.
The Unit Circle: Quiz
Question 2
• What is the Cos(315◦)?
A. √2/2
B. 1/2
C. - 1
D. 0
Correct!
Please go on to Question 3.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 2.
The Unit Circle: Quiz
Question 3
• What is the Cos(5π/6)?
A. -1/2
B. -1
C. 0
D. -√3/2
Correct!
Please go on to Question 4.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 3.
The Unit Circle: Quiz
Question 4
• What is the Sin(60◦)?
A. 0
B. -√3/2
C. √3/2
D. √2/2
Correct!
Please go on to Question 5.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 4.
The Unit Circle: Quiz
Question 5
• What is the Sin(210◦)?
A. -1/2
B. -√3/2
C. √3/2
D. 1/2
Correct!
Please go on to Question 6.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 5.
The Unit Circle: Quiz
Question 6
• What is the Cos(3π/2)?
A. 1
B. -1
C. 0
D. √2/2
Correct!
Please go on to Question 7.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 6.
The Unit Circle: Quiz
Question 7
• What is the Cos(135◦) ?
A. -√2/2
B. 1/2
C. √2/2
D. 1
Correct!
Please go on to Question 8.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 7.
The Unit Circle: Quiz
Question 8
• What is the Sin(2π)?
A. -1
B. 0
C. 1
D. 1/2
Correct!
Please go on to Question 9.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 8.
The Unit Circle: Quiz
Question 9
• What is the Sin(2π/3)?
A. √2/2
B. -1/2
C. 1/2
D. √3/2
Correct!
Please go on to Question 10.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 9.
The Unit Circle: Quiz
Question 10
• What is the Cos(180◦)?
A. 1
B. -1
C. -1/2
D. 0
Correct!
Please go on to Question 11.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 10.
The Unit Circle: Quiz
Question 11
• What is the Sin(330◦)?
A. √3/2
B. - √3/2
C. -1/2
D. 1/2
Correct!
Please go on to Question 12.
Incorrect
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points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 11.
The Unit Circle: Quiz
Question 12
• What is the Cos(π/3)?
A. √3/2
B. √2/2
C. -√3/2
D. 1/2
Correct!
Please go on to Question 13.
Incorrect
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points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 12.
The Unit Circle: Quiz
Question 13
• What is the Cos(5π/4)?
A. √2/2
B. -√2/2
C. 1/2
D. 0
Correct!
Please go on to Question 14.
Incorrect
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points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 13.
The Unit Circle: Quiz
Question 14
• What is the Sin(150◦)?
A. √3/2
B. -√3/2
C. 1/2
D. -1/2
Correct!
Please go on to Question 15.
Incorrect
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points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 14.
The Unit Circle: Quiz
Question 15
• What is the Cos(45◦)?
A. √2/2
B. √3/2
C. 1/2
D. 1
Correct!
Please go on to Question 16.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 15.
The Unit Circle: Quiz
Question 16
• What is the Sin(4π/3)?
A. -1/2
B. 1/2
C. √3/2
D. -√3/2
Correct!
Please go on to Question 17.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 16.
The Unit Circle: Quiz
Question 17
• What is the Sin(π/2)?
A. 0
B. -1
C. 1
D. 1/2
Correct!
Please go on to Question 18.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 17.
The Unit Circle: Quiz
Question 18
• What is the Sin(300◦)?
A. -1/2
B. √2/2
C. -√2/2
D. -√3/2
Correct!
Please go on to Question 19.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 18.
The Unit Circle: Quiz
Question 19
• What is the Cos(0◦)?
A. 0
B. 1
C. -1
D. √2/2
Correct!
Please go on to Question 20.
Incorrect
Remember to keep straight which points are positive and which
points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Angle Values
Sin(0◦)= 0
Sin(210◦)= -1/2
Cos(0◦)= 1
Cos(210◦)= -√3/2
Sin(30◦)= 1/2
Sin(225◦)= -√2/2
Cos(30◦)= √3/2
Cos(225◦)= -√2/2
Sin(45◦)= √2/2
Sin(240◦)= -√3/2
Cos(45◦)= √2/2
Cos(240◦)= -1/2
Sin(60◦)= √3/2
Sin(270◦)= -1
Cos(60◦)= 1/2
Cos(270◦)= 0
Sin(90◦)= 1
Sin(300◦)= -√3/2
Cos(90◦)= 0
Cos(300◦)= 1/2
Sin(120◦)= √3/2
Sin(315◦)= -√2/2
Cos(120◦)= -1/2
Cos(315◦)= √2/2
Sin(135◦)= √2/2
Sin(330◦)= -1/2
Cos(135◦)= -√2/2
Cos(330◦)= √3/2
Sin(150◦)= 1/2
Sin(360◦)= 0
Cos(150◦)= -√3/2
Cos(360◦)= 1
Sin(180◦)= 0
Cos(180◦)= -1
Return to Question 19.
The Unit Circle: Quiz
Question 20
• What is the Cos(π/6)?
A. 1/2
B. -1/2
C. -1
D. √3/2
Correct!
You have completed the quiz! Please ask your teacher to come
over and check to see if you passed.
Incorrect
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points are negative. If you need to review, click the review
button. If not, please try the question again.
The Unit Circle: Review
Radian Values
Sin(0)= 0
Sin(7π/6)= -1/2
Cos(0)= 1
Cos(7π/6)= -√3/2
Sin(π/6)= 1/2
Sin(5π/4)= -√2/2
Cos(π/6)= √3/2
Cos(5π/4)= -√2/2
Sin(π/4)= √2/2
Sin(4π/3)= -√3/2
Cos(π/4)= √2/2
Cos(4π/3)= -1/2
Sin(π/3)= √3/2
Sin(3π/2)= -1
Cos(π/3)= ½
Cos(3π/2)= 0
Sin(π/2)= 1
Sin(5π/3)= -√3/2
Cos(π/2)= 0
Cos(5π/3)= ½
Sin(2π/3)= √3/2
Sin(7π/4)= -√2/2
Cos(2π/3)= -1/2
Cos(7π/4)= √2/2
Sin(3π/4)√2/2
Sin(11π/6)= -1/2
Cos(3π/4)= -√2/2 Cos(11π/6)= √3/2
Sin(5π/6)= 1/2
Sin(2π)= 0
Cos(5π/6)= -√3/2 Cos(2π)= 1
Sin(π)= 0
Cos(π)= -1
Return to Question 20.
Great Job!!
You have completed the
lesson on the Unit Circle!!