Find the Exact Value tan(300)

Problem

tan(300^∘)

Solution

1. Identify the quadrant of the angle 300^∘ Since 270^∘<300^∘<360^∘ the angle lies in Quadrant IV.

2. Determine the sign of the tangent function in Quadrant IV. In this quadrant, the tangent of an angle is negative.

3. Calculate the reference angle (θ_R) For an angle in Quadrant IV, the reference angle is found by subtracting the angle from 360^∘

(θ_R)=360^∘−300^∘

(θ_R)=60^∘

4. Apply the reference angle property. The value of tan(300^∘) is equal to −tan(60^∘)

tan(300^∘)=−tan(60^∘)

5. Substitute the known exact value for tan(60^∘) which is √(,3)

tan(300^∘)=−√(,3)

Final Answer

tan(300^∘)=−√(,3)

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