Warm-Up 4/1
Fill in chart.
0
1
0
1
0
0
–1
–1
0
0
undefined
y
(0, 1)
(1, 0)
(– 1, 0)
x
(0, – 1)
undefined
Rigor:
You will learn how to evaluate and
determine sign of trig functions using
the Unit Circle.
Relevance:
You will be able to solve real world
problems using the Unit Circle.
Trig 4
The Unit Circle
The Unit Circle.
Unit Circle: a circle of radius 1 centered at
the origin in the xy-plane.
x  y 1
2
2
x
cos    x
1
y
sin    y
1
 cos ,sin  
1
x2
2
1
x3
2
x2
2
𝑥2 + 𝑥2 = 1
1
2
2𝑥 2 = 1
1
2
𝑥 =
2
𝑥=
𝑥=
1
2
1
2
=
2
2
12
+ 𝑥2 = 1
2
1
𝑥2 = 1 −
4
3
𝑥2 =
4
𝑥=
3
3
=
4
2
90
2𝜋
3
0
𝜋
1
2
3𝜋
4
𝜋
4
60
120
5𝜋
6
𝜋
3
135
150
–1 0
𝜋
𝜋
6
45
30
180
7𝜋
6
0
360
210
330
225
5𝜋
4
315
240
300
4𝜋
3
5𝜋
3
3𝜋
2
270
0 –1
7𝜋
4
0
2𝜋
11𝜋
6
1
0
Unit Circle
Draw in triangles to find the coordinates for each
point on the unit circle.
 cos ,sin  
1
45
60
30
1
3
1
2
1 2 3
2 2 2
2
2 1
2
(x, y)
Numerator
always 1 less
than denominator
Numerator
always 1 more
than denominator
Numerator
always 1
Numerator always
twice denominator
minus one
Example 1: Find the exact value of each
expression. If not defined, write undefined.
a. sin
7𝜋
6
b. cos
𝜋
3
c. tan
4𝜋
3
1
=−
2
1
=
2
3
−
2
3
2
∙ =
=
= 3
1 2
1
−
2
Periodic Functions
A function y = f(t) is periodic if there exist a
positive real number c such that f(t + c) = f(t) for
all values of t in the domain of t.
The smallest number c for which f is periodic is
called the period of t.
Example 2: Find the exact value of each expression.
a. cos
9𝜋
4
𝜋
𝜋
2
= cos + 2𝜋 = cos =
4
4
2
3
b. sin(−300°) = sin (60° −360°) = sin 60° =
2
c. tan
29𝜋
6
5𝜋
5𝜋
= tan
+ 4𝜋 = tan
=
6
6
1
2
3
−
2
=−
1
3
3
=−
3
Assignment:
Trig 4 WS 4-3 SGI, 1-8 all
I have 11th grade Pert Scores.
The Spring SAT Crash Course
When: April 9-10 and April 16-17
Time: 2:30-5:30
Where: Media Center
Cost: $10
Register: 3-207, by April 8.
th
7
Warm-Up 4/1
Find the exact values for each expression.
1. sin 60°
2. cos
𝜋
4
3
=
2
2
=
2
1
3. tan 30° = 2
3
2
1
3
=
=
3
3
Numerator
always 1 less
than denominator
Numerator
always 1 more
than denominator
Numerator
always 1
Numerator always
twice denominator
minus one
Example 1: Find the exact value of each
expression. If not defined, write undefined.
a. sin
7𝜋
6
b. cos
𝜋
3
c. tan
4𝜋
3
1
=−
2
1
=
2
3
−
2
3
2
∙ =
=
= 3
1 2
1
−
2
Periodic Functions
A function y = f(t) is periodic if there exist a
positive real number c such that f(t + c) = f(t) for
all values of t in the domain of t.
The smallest number c for which f is periodic is
called the period of t.
Example 2: Find the exact value of each expression.
a. cos
9𝜋
4
𝜋
𝜋
2
= cos + 2𝜋 = cos =
4
4
2
3
b. sin(−300°) = sin (60° −360°) = sin 60° =
2
c. tan
29𝜋
6
5𝜋
5𝜋
= tan
+ 4𝜋 = tan
=
6
6
1
2
3
−
2
=−
1
3
3
=−
3
Assignment:
Trig 4 WS 4-3 SGI, 1-8 all
I have 11th grade Pert Scores.
The Spring SAT Crash Course
When: April 9-10 and April 16-17
Time: 2:30-5:30
Where: Media Center
Cost: $10
Register: 3-207, by April 8.