Day 3 – Basic Concepts
Objectives:
At the end of the period, I should
be able to...
• Define Trigonometry
• Review the concept of an angle
• Identify the rotation of an angle
given the sign of its measure
Essential Questions
I will find the answer to the questions…
1. What is the best way to solve the
missing parts of a triangle?
2. How can we solve real-life problems
using trigonometric function and how?
Definition of Trigonometry
TRIGONOMETRY
“Trigonon”
“Metron”
Definition of Trigonometry
• Open your MLDs and go to your respective
link:
 10-E:
http://padlet.com/jose_calamlam/qkyz
1aycxlrf
• Answer the question “What is Trigonometry”.
• Write your group number in the title (red) and
then your answer in the body (black).
Definition of Trigonometry
“Trigonometry is a branch of
mathematics that studies
relationships involving sides and
angles of triangles”.
Question # 1
What is an angle? ____________________
How is it formed? _____________________
• ANGLE
It is formed by rotating a ray around its
endpoint. The ray in its initial position is called
the initial side of the angle, while the ray after
the rotation is the terminal side of the angle. The
endpoint of the ray is the vertex of the angle.
Question # 2
When is an angle in standard position?
Give the two conditions for an angle to be in
standard position.
1. ________________________________
2. ________________________________
When the vertex of an angle is the origin of the
coordinate plane and its initial side coincides with the
positive x – axis, the angle is said to be in standard
position.
y - axis
Terminal side
Vertex
x - axis
Initial side
Open TRIG WIZARD
Set the initial ray at 0
Click the + button on the bottom left
Stop the rotation by pressing the same
button
Click the - button on the bottom left
Question # 3
Complete the statements:
If the terminal side is rotating counter
clockwise, then the angle formed is
____________________
If the terminal side is rotating clockwise,
then the angle formed is
____________________
If the rotation of the terminal side is
counterclockwise, the angle is positive.
If the rotation is clockwise, the angle is negative.
Positive angle
Negative angle
Question # 4
How many degrees is one complete or full
counter clockwise rotation?
One unit of angle measure is the degree. One
full counterclockwise rotation measures 3600 ,
and one full clockwise rotation measures
- 3600.
Example # 1: How many degrees is 2/3 rotation
clockwise? If it is in standard position, in which
quadrant does its terminal side lie?
Solution:
= 2 ( - 1200) = - 2400
- 2400 + 360 = 1200 QII
Example # 2: How many degrees is 15/24 rotation
counterclockwise? If it is in standard position, in
which quadrant does its terminal side lie?
Open TRIG WIZARD
Given angle is inscribed in the cartesian plane,
observe the measures of the angles when it’s
terminal side is in …
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Question # 5
If an angle lies in the coordinate plane, what
are the measures of the angles in QI? QII?
QIII? QIV?
QI = between 00 to 900.
QII = between 900 to 1800.
QIII = between 1800 to 2700.
QIV = between 2700 to 3600.
Question # 6
What are coterminal angles?
Coterminal angles are angles in standard position
whose terminal sides coincide.
Example # 3: Sketch 600 and 4200 in the
coordinate plane and identify if they are coterminal
angles.
600
3600
Question # 7
How does one find an angle which is
coterminal with the given angle or a given
condition?
By adding or subtracting integral
multiples of 3600 .
Example # 4: Are – 1100 and – 8300 coterminal
angles? Why?
Homework 1
Questions
1. Convert 30° to radian measure.
2. Convert π/3 rad to degree measure.
Instructions:
1. Write your answers with solution in a one whole sheet of
pad paper.
2. Take a picture of your paper.
3. Submit the picture in your Google Classroom.
Homework 1
Refer to these links:
Degree  Radian:
https://www.khanacademy.org/math/trigonometry/unitcircle-trig-func/radians_tutorial/v/we-converting-degrees-toradians
Radian  Degree:
https://www.khanacademy.org/math/trigonometry/unitcircle-trig-func/radians_tutorial/v/we-converting-radians-todegrees
Extra examples:
https://www.khanacademy.org/math/trigonometry/unitcircle-trig-func/radians_tutorial/v/radian-and-degreeconversion-practice