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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