What is the secant of 5pi/4 and how was it determined to be -sqrt(2)?

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SUMMARY

The secant of 5π/4 is determined to be -√2 through the conversion of the angle to degrees, resulting in 225 degrees, which is located in the third quadrant. In this quadrant, the cosine value is negative, leading to a negative secant value. The reference angle of 45 degrees is utilized with the special triangle 45-90-45 to confirm this calculation. Thus, the conclusion is that sec(5π/4) = -√2 is correct.

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aisha
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I converted the given into degrees first and got 225 degrees. Then I sketched this in a circle with cartesian planes and saw that the reference angle =45 degrees so I used the special triangle 45-90-45 Since sec=1/cos-> cos is negative in the 3rd quadrant so for this question when I evaluated I got my answer to be -square root 2 is this right?
 
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Yes, your answer is correct. When converting 5pi/4 to degrees, you get 225 degrees which falls in the third quadrant. Since secant is positive in the first and fourth quadrants, and negative in the second and third quadrants, you correctly used the special triangle to find the reference angle and determined that the cosine is negative in the third quadrant. Therefore, the secant of 5pi/4 is -sqrt(2). Good job on using your knowledge of reference angles and special triangles to solve this problem!
 

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