Simplify tan(150)

Problem

tan(150)

Solution

1. Identify the angle in the coordinate plane. The angle 150 is in the second quadrant.

2. Determine the reference angle. The reference angle is calculated by subtracting the angle from 180

180−150=30

3. Apply the quadrant rule for the tangent function. In the second quadrant, the tangent of an angle is negative.

tan(150)=−tan(30)

4. Substitute the known value for the tangent of the reference angle.

tan(30)=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

tan(150)=−√(,3)/3

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