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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