Find the Exact Value tan((21pi)/4)

Problem

tan((21*π)/4)

Solution

1. Reduce the angle by subtracting multiples of the period of the tangent function, which is π

2. Calculate the number of periods by dividing the numerator by the denominator: 21/4=5.25

3. Subtract 5*π from the angle to find the reference angle in the first or third quadrant: (21*π)/4−5*π=(21*π)/4−(20*π)/4=π/4

4. Apply the identity tan(θ+n*π)=tan(θ) for any integer n

5. Evaluate the tangent of the resulting angle using the unit circle or special triangles.

6. Determine the value of tan(π/4) which is 1

Final Answer

tan((21*π)/4)=1

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