Chapter 7.1, Problem 2CFU

To determine

To explain: the reason behind naming the Pythagorean and opposite-angle identities.

Answer to Problem 2CFU

The Pythagorean identities come from the basic trigonometric functions and their applications to the right triangle.

The opposite angle identities come from the fact that negative angle is the opposite angle. The examples are as follows:

Explanation of Solution

Given information:

Pythagorean and opposite-angle identities

Calculation:

The Pythagorean identities come from the basic trigonometric functions and their applications to the right triangle. The Pythagorean identities are as follows:

  $\begin{array}{c}{\sin }^2\theta +{\cos }^2\theta =1\\ {\tan }^2\theta +1={\sec }^2\theta \\ 1+{\cot }^2\theta ={\csc }^2\theta \end{array}$

The opposite angle identities come from the fact that negative angle is the opposite angle. The examples are as follows:

  $\begin{array}{l}\sin (-A)=-\sin A\\ \cos \left(-A\right)=\cos A\end{array}$