Question

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

Answer 1

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

Answer 2

`-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`