Find the Exact Value sec(750)

Problem

sec(750^∘)

Solution

1. Identify the periodicity of the secant function. Since the secant function has a period of 360^∘ we can subtract multiples of 360^∘ from the angle to find its coterminal equivalent within the range [0^∘,360^∘)

2. Calculate the coterminal angle by subtracting 360^∘ twice.

750^∘−2*(360^∘)=750^∘−720^∘

750^∘−720^∘=30^∘

3. Rewrite the expression using the coterminal angle.

sec(750^∘)=sec(30^∘)

4. Apply the reciprocal identity for secant.

sec(30^∘)=1/cos(30^∘)

5. Substitute the known value for cos(30^∘) which is √(,3)/2

sec(30^∘)=1/√(,3)/2

6. Simplify the fraction by multiplying by the reciprocal.

sec(30^∘)=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

Final Answer

sec(750^∘)=(2√(,3))/3

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