How do you evaluate sec((5pi)/4)?

2 Answers
Helen D.
Mar 19, 2016

secant is the reciprocal of COSINE

so sec (5pi)/4= 1/(cos((5pi)/4)
Now the angle is in 3rd quadrant and cosine is negative in the 3rd quadrant (CAST rule).

this means that the 1/(cos((5pi)/4) = -1/(cos((pi)/4)
and since cos((pi)/4)=1/sqrt2 , your result is that

sec (5pi)/4=-sqrt2/1

hope this helps

Nghi N.
Mar 19, 2016

-sqrt2

Explanation:

sec ((5pi)/4) = 1/(cos ((5pi)/4)).
Find cos ((5pi)/4)
Trig unit circle and trig table give -->
cos ((5pi)/4) = cos ((3pi)/4) = -sqrt2/2
Therefor:
sec ((5pi)/4) = - 2/sqrt2 = - sqrt2

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