Find the exact values of the sine, cosine, and tangent of the angle. 7π/12 = π/3 + π/4.

Solution:

Given the angle in radians as 7π/12

The angle 7π/12 can be written as π - 5π/12

sin(7π/12) = sin(π - 5π/12) = sin(5π/12) = 0.96

We know that sin(π - θ) = sinθ

cos(7π/12) = cos(π - 5π/12) = -cos(5π/12) = -0.25

We know that cos(π - θ) = -cosθ

Using the trigonometric ratio, we know that tanA = sinA/cosA

tan(7π/12) = sin(7π/12)/cos(7π/12) = 0.96/-0.25 = -3.84

Find the exact values of the sine, cosine, and tangent of the angle. 7π/12 = π/3 + π/4.

Summary:

The exact values of sine, cosine, and tangent for the angle 7π/12 are 0.96, -0.25, and -3.84 respectively.