1. Lesson 1

1.7. Explore 3

Mathematics 30-1 Module 5

Module 5: Trigonometry Applications and Identities

 

In Try This 3 you may have seen that the slope of the terminal arm in standard position at angle θ is equal to tan θ.

 

This diagram shows a right triangle with hypotenuse a, sides 1 and tan theta and angle theta. Beneath it is written slope of A equals rise over run equals tan theta over 1 equals tan theta.

 

In Try This 4 you will explore a relationship between sine, cosine, and tangent.

 

Try This 4

 

Recall from Module 4 that cos θ and sin θ can be defined as the x- and y-coordinates of the unit circle, respectively. Look at the following diagram.

 

This diagram shows the lengths representing sin theta, cos theta, and tan theta on the unit circle.

  1. Use the diagram and your knowledge of similar triangles to determine a relationship between sin θ, cos θ, and tan θ. hint
  2. Consider the following graph that shows y = sin x, y = cos x, and y = tan x.

    This graph shows the functions y is equal to the sine of x, y is equal to the cosine of x, and y is equal to the tangent of x.
    1. What is the value of tan θ when sin θ = 0?
    2. What is the value of tan θ when cos θ = 0?

course folder Save your responses in your course folder.

 

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With a partner or group, discuss the following question based on the relationship you determined in Try This 4.

In terms of the graph in question 2 of Try This 4, how can you explain the relationship you determined in question 1?

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

Recall that the following relationship is true for similar triangles.

 

 

The diagram shows that the ratio of corresponding sides of similar triangles is equal.