3) Determine an exact value for the expression: sin(5pi )/(4)-cos(11pi )/(6)cot(pi )/(3)

Question

Answer 1

To solve the expression

, we evaluate each trigonometric function separately.1. **Evaluate

:** The angle

is in the third quadrant where sine is negative. It is equivalent to

.

2. **Evaluate

:** The angle

is in the fourth quadrant where cosine is positive. It is equivalent to

.

3. **Evaluate

:**

. For

:

4. **Combine the results:** Substitute the evaluated values into the original expression:

Simplify the second term:

Therefore, the expression becomes:

Thus, the exact value of the expression is:

Question