Question

find the value of sin pi by 8

Answer 1

sin(π8)

Since

π8 is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

π8 is not an exact angle

First, rewrite the angle as the product of

12

12 and an angle where the values of the six trigonometric functions are known. In this case,

π8

π8 can be rewritten as

(12)⋅π4

(12)⋅π4.sin((12)⋅π4)

sin((12)⋅π4)

Use the half-angle identity for sine to simplify the expression. The formula states that

sin(θ2)=√1−cos(θ)2

sin(θ2)=1-cos(θ)2.

⎷1−cos(π42)