Question

Find the exact value by using half-angle identity.

sin(7pi/8)

Answer 1

Stick to the more-common angles — the ones that have exact values or are multiples of 30 and 45. Substitute that angle into the half-angle identity for sine. Because the sine of 15 degrees is a positive value, the sign in front of the radical becomes +. Fill in the function values and simplify the answer.

Answer 2

-1

Explanation:

According to half angle,

Sin(theta) = sin{theta/2+theta/2}

=Sin(theta/2)cos(theta/2)+cos(theta/2)Sin(theta/2)

= 2Sin(theta/2)cos(theta/2)

If theta = 7Π/2 and;

Sin(theta) = 2Sin(theta/2)cos(theta/2)

Sin(7Π/4) = 2(sin7Π/4)cos(7Π/4)

If Πrad = 180°

7Π/4 rad = 7/4×180°

7Π/4 rad = 315° (in degrees)

Sin(7Π/4) = 2sin315°cos315°

Sin(7Π/4) = 2(-0.5)

Sin(7Π/4) = -1.0

The exact value is -1