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

Want more problems? Check here!