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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