Chapter 8.2, Problem 51E

To determine

Find the value of $\sin 225°$ .

Answer to Problem 51E

  $-0.7071$

Explanation of Solution

Given information:

Use sum or difference identities.

Calculation:

Consider, the angle $\sin 225°$

It is equal to $180°+45°$

Now use sum identity, $\sin \left(A+B\right)=\sin A\cos B+\cos A\sin B$

Substitute $A=180°,B=45°$

  $\begin{array}{l}\sin \left(180°+45°\right)=\sin 180°\cos 45°+\cos 180°\sin 45°\\ \sin \left(225°\right)=0\times 0.7071+-1\times 0.7071\\ \sin \left(225°\right)=-0.7071\end{array}$

Hence, the value of $\sin 225°$ is $-0.7071$ .