Question

How do you use the half angle formula to determine the exact values of the sine, cosine, and tangent `15^circ`?

Answer 1

Use trig table, unit circle, and trig identities: -->
`2sin^2 15 = 1 - cos 30 = 1 - sqrt3/2 = (2 -sqrt3)/2`
`sin 15 = +- sqrt(2 - sqrt3)/2`
Since sin 15 is pisitive, then, take the positive value.
`sin 15 = sqrt(2 - sqrt3)/2`
`2cos^2 15 = 1 + cos 30 = (1 + sqrt3/2) = (2 + sqrt3)/2`
`cos 15 = sqrt(2 + sqrt3)/2` (because cos 15 is > 0)
`tan 15 = sin/(cos) = sqrt(2 - sqrt3)/(sqrt(2 + sqrt3)`