Find the Exact Value sec(855)

Problem

sec(855)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is between 0 and 360

855−2*(360)=855−720=135

2. Identify the quadrant for 135 Since 90<135<180 the angle is in Quadrant II.

3. Determine the reference angle for 135 in Quadrant II.

180−135=45

4. Apply the reciprocal identity for secant.

sec(135)=1/cos(135)

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

cos(135)=−cos(45)=−√(,2)/2

6. Calculate the reciprocal to find the secant value.

sec(135)=1/(−√(,2)/2)=−2/√(,2)

7. Rationalize the denominator by multiplying the numerator and denominator by √(,2)

−(2√(,2))/2=−√(,2)

Final Answer

sec(855)=−√(,2)

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