Chapter 13.7, Problem 9WE

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 9WE

The simplified form is $\sin 210°$ and the exact value is $-\frac{\sqrt{3}}{2}$ .

Explanation of Solution

Given:

The given function is $\sin 130°\cos 80°+\cos 130°\sin 80°$ .

Calculation:

Consider the given function is,

  $\sin 130°\cos 80°+\cos 130°\sin 80°$

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,

  $\sin \left(130°+80°\right)=\sin 210°$

Solve $\sin 210°$ by trigonometric identity as,

  $\begin{array}{c}\sin 210°=\sin \left(180°+30°\right)\\ =-\sin 30°\\ =-\frac{\sqrt{3}}{2}\end{array}$