To find the exact values of the sine, cosine, and tangent of the angle 7π/12 − π/3 − π/4, we first need to simplify the expression.
1. **Convert angles to a common denominator**: The common denominators for the fractions are 12.
- Convert π/3:
π/3 = 4π/12 - Convert π/4:
π/4 = 3π/12
2. **Substituting back in**:
So we have:
7π/12 – 4π/12 – 3π/12 = 0
3. **Evaluate trigonometric functions**: The angle simplifies to 0 radians. Now we can find the sine, cosine, and tangent:
- sin(0) = 0
- cos(0) = 1
- tan(0) = 0
So, the exact values are:
- sin(7π/12 – π/3 – π/4) = 0
- cos(7π/12 – π/3 – π/4) = 1
- tan(7π/12 – π/3 – π/4) = 0