Find the Exact Value tan(540)

Problem

tan(540)

Solution

1. Identify the angle in terms of its reference angle by subtracting multiples of 360 to find a coterminal angle within the standard 0 to 360 range.

540−360=180

2. Apply the definition of the tangent function, which is the ratio of the sine to the cosine of the angle.

tan(180)=sin(180)/cos(180)

3. Evaluate the sine and cosine values at 180 using the unit circle, where the coordinates are (−1,0)

sin(180)=0

cos(180)=−1

4. Substitute these values into the tangent ratio and simplify the fraction.

tan(180)=0/(−1)=0

Final Answer

tan(540)=0

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