Find the Exact Value tan(-3pi)

Problem

tan(−3*π)

Solution

1. Identify the periodicity of the tangent function. The tangent function has a period of π which means tan(θ+n*π)=tan(θ) for any integer n

2. Simplify the angle by adding multiples of the period. Since we want to find the value at −3*π we can add 3*π to the angle.

tan(−3*π)=tan(−3*π+3*π)

tan(−3*π)=tan(0)

3. Apply the definition of tangent in terms of sine and cosine.

tan(0)=sin(0)/cos(0)

4. Substitute the known values for sine and cosine at 0 We know that sin(0)=0 and cos(0)=1

tan(0)=0/1

tan(0)=0

Final Answer

tan(−3*π)=0

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