Question

Find exact value using sum or difference identity: sin 13 pi/12

Answer 1

The value of the angle in degrees is -0.2588

Here, we want to find the excat value of the given trigonometric identity

What we are told here is to use the sum of difference identity

We have this as follows

$\begin{gathered} \sin \text{ }\frac{13\pi}{12}\text{ = sin(}\frac{16\pi}{12}-\frac{3\pi}{12}) \\ \\ we\text{ have;} \\ \sin \text{ (}\alpha+\beta)\text{ = sin }\alpha\cos \beta-cos\alpha\sin \text{ }\beta \\ \\ \sin \text{ }\frac{13\pi}{12}\text{ = sin(}\frac{16\pi}{12}-\frac{3\pi}{12})\text{ = sin }\frac{16\pi}{12}\cos \frac{3\pi}{12}-\cos \frac{16\pi}{12}\sin \text{ }\frac{3\pi}{12} \\ \end{gathered}$

Substituting the individual degree values, we have;

$-0.6124-(-0.3536)\text{ = -0.6124}+0.3536=\text{ -0.2588}$