find the function values

Question

sin²π⁄12

Answer 1

To find the value of sin²(π/12), we can use the Pythagorean identity sin²(x) + cos²(x) = 1

As found from your last question, cos(π/12) = √(2 + √3)/2, so this means cos²(π/12) = (2 + √3)/4.

Hence, our equation becomes:

sin²(π/12) + (2 + √3)/4 = 1

sin²(π/12) = 1 - (2 + √3)/4

sin²(π/12) = 4/4 - (2 + √3)/4

sin²(π/12) = (4 - 2 - √3)/4

sin²(π/12) = (2 - √3)/4

Therefore, the value of sin²(π/12) is (2 - √3)/4.

Hope this helped!