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Lesson 4

1. Lesson 4

1.9. Explore 5

Mathematics 30-1 Module 4

Module 4: Foundations of Trigonometry

 

Try This 3

 

In Try This 3 you will determine the exact value for

  1. Draw a diagram of the angle  in standard position.
  2. Choose either Part A or Part B to determine the exact value.

    Part A: Look up  on the unit circle from Lesson 3.

    Part B: Determine the angle from the terminal arm to the x-axis; then choose one of the reference triangles to help determine the exact value.

  3. Write the exact value for

course folder Save your responses in your course folder.

 

Share 2

 

With a partner or group, discuss the strategy you used in Try This 3. Explain any similarities or differences in your strategies, and describe which strategy you prefer and why.

 

course folder If required, save a record of your discussion in your course folder.


tip

A term that you will use is reference angle, θR. This angle is the acute, positive angle between the x-axis and the terminal arm.

 

 
This diagram shows two terminal arms on two unit circles. The angle between the x-axis and the terminal arm is labelled reference angle.



Remember to look at which quadrant is in to determine whether the value is positive or negative.

 

 
Angle 4 pi divided by 3 is drawn in standard position with the reference triangle with angle pi divided by 3 and radius of 1 in quadrant 3. The sides of the reference triangle are labelled to match the x and y values in quadrant three. The y value is negative square root of 3 divided by 2, and the x value is negative one half.
Remember that the y-coordinate for the point at  is the value of sin .