Question

Hi! Can someone help check this for me and see if I'm doing it right? Thanks!! :)

Directions: Use the Half-Angle formulas to determine the exact value of sin(pi/12). Here's what I have:

π/12 = ( 180° ) / 12 = 15°.

= sin ( π/12 )

= sin 15°

= sin ( 45° - 30°)

= sin 45°· cos 30° - cos 45°· sin 30°

= (1/√2)·(√3 /2 ) - (1/√2)·(1/2)

= ( √3 - 1 ) / (2√2)

Answer 1

Even though you got the correct answer you did not follow the required method.
(That's like winning a 100 m backstroke race by using the butterfly stroke , you would be DQ'd)

It said to use the Half-Angle formula
There are two,
sin (2A) = 2sinAcosA
and
cos(2A) = cos^2 A - sin^2 A = 1 - 2sin^2 A = 2cos^2 A - 1

I will use
cos(2A) = 1 - 2sin^2 A
cos 30° = 1 - 2sin^2 15°
2 sin^2 15 = 1 - √3/2 = (2-√3)/2
sin^2 15 = (2 - √3)/4
sin 15 = √(2 - √3) /2

Check: by using your calculator to find sin15 , and evealutationg my answer to show they are equal

even though this answer looks different from yours, use your calculator to show that it is the same as your answer

Answer 2

I interpret the instruction to use the Half-Angle formula as

sin(15°) = √((1-cos30°)/2)
= √((1-√3/2)/2
= √(2-√3)/2
= (√6-√2)/2

Granted, the half- and double-angle formulas are two sides of the same coin, but ...