Chapter 13.7, Problem 8WE

To determine

To find: The simplified form of the trigonometric function of the single angle then given the exact value if possible.

Answer to Problem 8WE

The simplified form is $\sin 45°$ and the exact value is $\frac{1}{2}$ .

Explanation of Solution

Given:

The given function is $\sin 50°\cos 5°-\sin 5°\cos 50°$ .

Calculation:

Consider the given function is,

  $\sin 50°\cos 5°-\sin 5°\cos 50°$

Consider the above trigonometric identity.

  $\sin \left(a-b\right)=\sin a\cos b-\sin b\cos a$

Then, the given function is written as,

  $\begin{array}{c}\sin \left(50°-5°\right)=\sin 45°\\ =\frac{1}{2}\end{array}$