Find the Exact Value tan(330)

Problem

tan(330)

Solution

1. Identify the reference angle by finding the difference between 330 and the nearest x-axis boundary, which is 360

(θ_ref)=360−330=30

2. Determine the quadrant in which 330 lies. Since 270<330<360 the angle is in Quadrant IV.

3. Determine the sign of the tangent function in Quadrant IV. In this quadrant, x is positive and y is negative, so tan(θ) is negative.

tan(330)=−tan(30)

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

tan(30)=1/√(,3)

5. Rationalize the denominator of the value.

1/√(,3)=√(,3)/3

6. Apply the negative sign determined in step 3 to find the final value.

tan(330)=−√(,3)/3

Final Answer

tan(330)=−√(,3)/3

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