Thread: Exact value of sin 17pi/12

12.a) Determine an exact value for sin 17pi/12.

b) Determine the answer to part a) using a different method.

So as of now I only know one way to do it.. which is using the compound angle formula. This is what I did:

sin(x+y) = sinxcosy+cosxsiny
sin(2pi/3 + 3pi/4) = sin(2pi/3)cos(3pi/4)+cos(2pi/3)sin(3pi/4)
=(sqr3/2)(-1/sqr2) + (-1/2)(1/sqr2)
=-sqr3/2sqr2 + -1/2sqr2
=-sqr3-1/2sqr2

This is the correct answer. Any ideas on what a second way of finding the exact value of sin 17pi/12 would be? The easier the better haha.

Originally Posted by kmjt

12.a) Determine an exact value for sin 17pi/12.

b) Determine the answer to part a) using a different method.

So as of now I only know one way to do it.. which is using the compound angle formula. This is what I did:

sin(x+y) = sinxcosy+cosxsiny
sin(2pi/3 + 3pi/4) = sin(2pi/3)cos(3pi/4)+cos(2pi/3)sin(3pi/4)
=(sqr3/2)(-1/sqr2) + (-1/2)(1/sqr2)
=-sqr3/2sqr2 + -1/2sqr2
=-sqr3-1/2sqr2

This is the correct answer. Any ideas on what a second way of finding the exact value of sin 17pi/12 would be? The easier the better haha.

You can check the answer with your calculator:

Code:

>sin(17*pi/12)
    -0.965926 
>
>(sqrt(3)/2)*(-1/sqrt(2))+(-1/2)*(1/sqrt(2))
    -0.965926 
>

Your poor use of brackets makes it difficult to tell if you have simplified correctly.

For a second method use:



Now proceed as before.

CB

Hello, kmjt!

12 (a) Determine an exact value for: .

. . (b) Determine the answer to part (a) using a different method.

Use the identity: .


Since is in Quadrant 3, is negative.


We have: .

. . . . . . . .

I'm not quite sure whats going on there How is the stuff changing in the square root? Like at first the top is 1 - cos 17pi6 then in the next part its cos 5pi/6?