Find the Exact Value tan(-300 degrees )

Problem

tan(−300^∘)

Solution

1. Find a coterminal angle by adding 360^∘ to the given angle to find its equivalent position within the standard 0^∘ to 360^∘ range.

−300^∘+360^∘=60^∘

2. Identify the reference angle and the quadrant. Since 60^∘ is in the first quadrant, the reference angle is 60^∘

θ=60^∘

3. Determine the sign of the tangent function in the first quadrant. In Quadrant I, all trigonometric functions are positive.

tan(60^∘)>0

4. Evaluate the tangent of the reference angle using the known values for special angles.

tan(60^∘)=√(,3)

Final Answer

tan(−300^∘)=√(,3)

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