Question

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

Answer 1

The better way is, first we have to find the equivalent in degrees


`2\pi=360\º`


`(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)&=&(1)/(2)\\\\sin(45\º)&=&cos(45\º)&=&(√(2))/(2)}\end{matrix}\\\\cos(30\º)&=&(√(3))/(2)\end{matrix}`

now we replace this values


`sin(-15\º)=(1)/(2)*(√(2))/(2)-(√(2))/(2)*(√(3))/(2)`


`sin(-15\º)=(√(2))/(4)-(√(6))/(4)`


`\boxed{\boxed{sin(-15\º)=sin(345\º)=(√(2)-√(6))/(4)}}`