Question

Find sin(17π/12) exactly.

I think it has to do something with splitting 17π/12 into π/3 + π/4 + 5π/6 and then using the sin/cos angle sum identities. Though when I tried this, it got complicated really quickly, so I'm not sure if this is the method I should be using.

Answer 1

Please refer to the photo taken.

Answer 2

-(√2 +√6)/4

Explanation:

You want the exact value of sin(17π/12).

Sine of sum

The sine can be written as ...

sin(17π/12) = sin(π +5/12π)

= -sin(5/12π) = -sin(2/12π +3/12π)

= -sin(π/6 +π/4)

= -(sin(π/6)cos(π/4) +cos(π/6)sin(π/4))

= -((1/2)(√2/2) +(√3/2)(√2/2))

= -(√2 +√6)/4

The sine of 17π/12 is -(√2+√6)/4.