Find the Exact Value tan(390)

Problem

tan(390)

Solution

1. Identify the angle as being greater than 360 and find its coterminal angle within the range [0,360)

2. Subtract 360 from the given angle to find the coterminal equivalent.

θ=390−360

θ=30

3. Apply the property that trigonometric functions of coterminal angles are equal.

tan(390)=tan(30)

4. Evaluate the tangent of the reference angle using the unit circle or special right triangles.

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

tan(30)=(1/2)/(√(,3)/2)

5. Simplify the fraction by rationalizing the denominator.

tan(30)=1/√(,3)

tan(30)=√(,3)/3

Final Answer

tan(390)=√(,3)/3

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