Question

Find the exact value by using a half-angle identity.
sin(5pi/12)

Answer 1

help me guys!!!:(

Answer 2

OK, so first of all notice that 5pi/12 is just half of 10pi/12 which is 5pi/6 (that's something we can actually calculate)

Answer 3

We need to use the half angle formula for sin, let me look that up

Answer 4

sin(B/2) = ± sqrt([1 − cos B] / 2)

Answer 5

so sin(5pi/12) = ±sqrt([1 - cos(5pi/6)] / 2)

Answer 6

= ±sqrt([1 - (sqrt(3)/2)] / 2)

Answer 7

since 5pi/12 is in the first quadrant, we know that sin will be positive so choose the positive value.

Answer 8

@jtvatsim so is it the same thing as 1/2sqrt(2+sqrt3)?

Answer 9

you got it! :)

Answer 10

@jtvatsim it wont be 1/2sqrt(2-sqrt3) right??

Answer 11

correct, that would be the negative answer which we don't want. :)

Answer 12

a good resource to use to look up quick math answers is wolframalpha.com, that's what I used to check.