Find the Exact Value sec(330 degrees )

Problem

sec(330)

Solution

1. Identify the reference angle by finding the difference between 330 and the nearest x-axis value, which is 360

360−330=30

2. Determine the quadrant of the angle. Since 330 is between 270 and 360 it lies in Quadrant IV.

3. Apply the sign rule for the secant function. In Quadrant IV, the cosine function is positive, and since sec(θ)=1/cos(θ) the secant function is also positive.

sec(330)=sec(30)

4. Evaluate the secant of the reference angle using the reciprocal identity sec(θ)=1/cos(θ)

cos(30)=√(,3)/2

5. Calculate the reciprocal to find the exact value.

sec(30)=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

Final Answer

sec(330)=(2√(,3))/3

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