Find the Exact Value tan(600)

Problem

tan(600^∘)

Solution

1. Find the coterminal angle by subtracting multiples of 360^∘ until the angle is between 0^∘ and 360^∘

600^∘−360^∘=240^∘

2. Identify the quadrant for 240^∘ Since 180^∘<240^∘<270^∘ the angle lies in Quadrant III.

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

240^∘−180^∘=60^∘

4. Determine the sign of the tangent function in Quadrant III. In Quadrant III, tangent is positive.

tan(600^∘)=tan(60^∘)

5. Evaluate the exact value using the known trigonometric values for 60^∘

tan(60^∘)=√(,3)

Final Answer

tan(600^∘)=√(,3)

Want more problems? Check here!