Simplify tan(-300)

Problem

tan(−300^∘)

Solution

1. Apply the odd function property of the tangent function, which states that tan(−θ)=−tan(θ)

tan(−300^∘)=−tan(300^∘)

2. Find the coterminal angle or use the periodicity of the tangent function (180^∘ to bring the angle into the first or second quadrant.

300^∘=360^∘−60^∘

3. Determine the reference angle and the sign of the tangent function in the fourth quadrant. Since 300^∘ is in the fourth quadrant, the tangent is negative.

tan(300^∘)=−tan(60^∘)

4. Substitute this back into the expression from step 1.

−tan(300^∘)=−(−tan(60^∘))

tan(60^∘)

5. Evaluate the tangent of the common angle 60^∘ using the unit circle or special triangles.

tan(60^∘)=√(,3)

Final Answer

tan(−300^∘)=√(,3)

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