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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