   Chapter 4.1, Problem 49PS ### Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
ISBN: 9781305652224

#### Solutions

Chapter
Section ### Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
ISBN: 9781305652224
Textbook Problem

# Make a diagram of the unit circle with an angle θ in QI and its supplement 180 ° − θ in QII. Label the point on the terminal side of θ and the unit circle with ( x , y ) and the point on the terminal side of 180 ° − θ and the unit circle with ( − x , y ) . Use the diagram to show the following.Show that tangent is an odd function.

To determine

To prove:

Tan is an odd function.

Explanation

Proof:

Let us first make a diagram using the given description:

From triangle in first quadrant, we can set:

tanθ=yx

Similarly, using the triangle in forth quadrant, we can set:

tan(θ)=yx

From these two equations, we can write:

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