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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