Find the Exact Value tan(-330 degrees )

Problem

tan(−330)

Solution

1. Find a coterminal angle by adding 360 to the given angle to find an equivalent angle within the standard 0 to 360 range.

θ=−330+360=30

2. Identify the reference angle and the quadrant. Since 30 is in the first quadrant, the reference angle is 30 and the tangent function is positive.

tan(−330)=tan(30)

3. Apply the trigonometric value for the tangent of 30 using the unit circle or a special right triangle.

tan(30)=sin(30)/cos(30)

4. Substitute the known values for sine and cosine.

tan(30)=(1/2)/(√(,3)/2)

5. Simplify the fraction by canceling the denominators.

tan(30)=1/√(,3)

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

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

tan(−330)=√(,3)/3

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