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

Question

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

anonymous · Answer

help me guys!!!:(

jtvatsim · Answer

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)

jtvatsim · Answer

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

jtvatsim · Answer

sin(B/2) = ± sqrt([1 − cos B] / 2)

jtvatsim · Answer

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

jtvatsim · Answer

= ±sqrt([1 - (sqrt(3)/2)] / 2)

jtvatsim · Answer

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

anonymous · Answer

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

jtvatsim · Answer

you got it! :)

anonymous · Answer

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

jtvatsim · Answer

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

jtvatsim · Answer

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