Question

What two angles would I need to add together to get sin(17pi/12)
The angles have to be from the pi circle

Sum and difference formulas hw
Will fan and medal

Answer 1

The key thing to do is split up 17pi/12 as a sum/difference of two known unit circle values.

17pi/12 = 9pi/12 + 8pi/12 = 3pi/4 + 2pi/3

Now, use the cosine addition identity.

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

cos(3pi/4 + 2pi/3) = cos(3pi/4)cos(2pi/3) - sin(3pi/4)sin(2pi/3)
= [ -sqrt(2)/2 ] [ -1/2 ] - [ sqrt(2)/2 ] [ sqrt(3)/2 ]
= [ sqrt(2)/4 ] - [ sqrt(2)sqrt(3) / 4 ]

Merging the radicals in the second fraction,

= [ sqrt(2)/4 ] - [ sqrt(6)/4 ]

Putting under a common denominator,

= [sqrt(2) - sqrt(6)] / 4

Answer 2

Thank you so much, can you help me with one more, I'll try not take up too much time @Hannah_Waller

Answer 3

I can try

Answer 4

whats the question? @minisweet4

Answer 5

sec (-pi/12)

Answer 6

im not real sure on this one sorry :(

Answer 7

It's okay, thanks for the help