sisca05st
2

# Suppose theta= 11pi/12. How do you use the sum identity to find the exact value of sin theta?

katiebabyyy

The better way is, first we have to find the equivalent in degrees $2\pi=360\º$ $\frac{11\pi}{12}=345\º$ now we can change this value to $-15\º$ how do we get an angle like this?! $30\º-45\º=-15\º$ then $sin(30\º-45\º)=sin(30\º)*cos(45\º)-sin(45\º)*cos(30\º)$ $\begin{Bmatrix}sin(30\º)&=&\frac{1}{2}\\\\sin(45\º)&=&cos(45\º)&=&\frac{\sqrt{2}}{2}}\end{matrix}\\\\cos(30\º)&=&\frac{\sqrt{3}}{2}\end{matrix}$ now we replace this values $sin(-15\º)=\frac{1}{2}*\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}$ $sin(-15\º)=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4}$ $\boxed{\boxed{sin(-15\º)=sin(345\º)=\frac{\sqrt{2}-\sqrt{6}}{4}}}$