Find the Exact Value tan(570)

Problem

tan(570)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the standard 0 to 360 range.

570−360=210

2. Determine the quadrant of the angle 210 Since 180<210<270 the angle lies in Quadrant III.

3. Find the reference angle for an angle in Quadrant III using the formula (θ_ref)=θ−180

210−180=30

4. Determine the sign of the tangent function in Quadrant III. Tangent is positive in the third quadrant.

tan(210)=tan(30)

5. Evaluate the exact value of the tangent of the reference angle.

tan(30)=√(,3)/3

Final Answer

tan(570)=√(,3)/3

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