Find the Exact Value tan(750)

Problem

tan(750)

Solution

1. Identify the periodicity of the tangent function, which repeats every 180

2. Subtract multiples of 180 from the angle to find a coterminal angle within the standard range of 0 to 180

750−4⋅180=750−720

750−720=30

3. Apply the trigonometric identity tan(θ+n⋅180)=tan(θ) to rewrite the expression.

tan(750)=tan(30)

4. Evaluate the tangent of the reference angle using the known values for special angles.

tan(30)=1/√(,3)

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

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

tan(750)=√(,3)/3

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