Explore

 

In Try This 1 you may have noticed the following relationships:

• cos θ = x
• sin θ = y
• 

Are these relationships only valid for points on a unit circle? In Try This 2 you will explore these relationships further in order to help answer this question.

 

Try This 2

 

Use Trigonometric Ratios and the Unit Circle to answer the following questions. You can change theta by using the angle slider.

 

1. Write an expression for cos θ in terms of the line segments of the triangle—OA, OP, or AP. You may want to click the Hint checkbox in the applet.
2. Write an expression for sin θ in terms of the line segments of the triangle—OA, OP, or AP.
3. Write an expression for tan θ in terms of the line segments of the triangle—OA, OP, or AP.
4. What is the length of line segment OP, since this is the unit circle? Replace line segment OP with this value in your previous answers.
5. The length of OA is the same value as the x-coordinate of point P, and the length of AP is the same value as the y-coordinate of point P. Replace OA and AP with x and y in your expressions from question 4.
6. Use your answers from question 5 to write expressions for the coordinates of point P.
7. Would the expressions in question 6 be different for a point on a circle when the radius is not 1? Why or why not?

 Save your responses in your course folder.