Verified answer

225 degrees is correct, but the unit circle value there is (-sqrt(2)/2, -sqrt(2)/2). Remember all points on the unit circle are distance 1 from the origin. The point (-1/2,-1/2) is sqrt((-1/2)^2 + (-1/2)^2) = sqrt(1/4 + 1/4) = sqrt(1/2) away from the origin. Using that point should give you the correct answer.

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sec(5π/4) = 1/cos(5π/4)

Now, 5π/4 radians is π/4 radians past 180°

so that it is a 3rd quadrant angle and its reference angle is π/4.

Cosine is negative in the 3rd quadrant so we have

cos(5π/4)  =  -cos(π/4) =  -1/√ ̅2̅ .

It follows that

sec(5π/4) = 1/cos(5π/4) = 1/(-cos(π/4))  = 1/(-1/√ ̅2̅ )  =  -√ ̅2̅

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