Find the Exact Value sec(570)

Problem

sec(570)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the standard 0 to 360 range.

570−360=210

2. Identify the quadrant for 210 Since 180<210<270 the angle lies in Quadrant III.

3. Determine the reference angle by subtracting 180 from the angle.

210−180=30

4. Apply the reciprocal identity for secant, which is sec(θ)=1/cos(θ)

sec(210)=1/cos(210)

5. Evaluate the cosine of the angle. In Quadrant III, cosine is negative.

cos(210)=−cos(30)

cos(210)=−√(,3)/2

6. Calculate the secant by taking the reciprocal of the cosine value.

sec(210)=1/(−√(,3)/2)

sec(210)=−2/√(,3)

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

−2/√(,3)⋅√(,3)/√(,3)=−(2√(,3))/3

Final Answer

sec(570)=−(2√(,3))/3

Want more problems? Check here!