Evaluate tan(150 degrees )

Problem

tan(150)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest x-axis.

(θ_ref)=180−150=30

2. Determine the quadrant of the angle 150 Since 90<150<180 the angle lies in Quadrant II.

3. Determine the sign of the tangent function in Quadrant II. In this quadrant, sine is positive and cosine is negative, so tangent is negative.

tan(150)=−tan(30)

4. Evaluate the tangent of the reference angle using known trigonometric values.

tan(30)=1/√(,3)

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

1/√(,3)=√(,3)/3

6. Combine the value with the determined sign.

tan(150)=−√(,3)/3

Final Answer

tan(150)=−√(,3)/3

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