# How to find all values of xx for which secx=−1\sec x=-1 is true?

Find all values of x for which the following is true.
secx=−1\sec x = -1

a) د€ + 2kد€
b) (د€/4) + 2kد€
c) 2kد€
d) (د€/2) + kد€
e) -(د€/3) + 2kد€

I know that secθ=1cosθ\sec \theta =\frac 1 {\cos \theta}. I don’t know what to do after that. I think the unit circle is involved somehow.

This is for my online trigonometry class, it’s a homework problem and I can’t figure it out. Any help is much appreciated.

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For a): what is cos(π)\cos(\pi)? What is cos(π+2kπ)\cos(\pi + 2 k \pi)?
– dxiv
Oct 20 at 23:41

cos(د€) = -1. I don’t know what the k means so I don’t know how to answer your other question.
– user7045242
Oct 20 at 23:46

In trig contexts like this one it’s usually defined (or assumed) that k∈Zk \in \mathbb{Z} is an integer, so 2kπ2 k \pi is an integer multiple of 2π2 \pi.
– dxiv
Oct 20 at 23:49

I still don’t understand how to figure out cos(د€ + 2kد€). What does k equal? Sorry, bad at math.
– user7045242
Oct 20 at 23:51

1

@dxiv Oh okay. Thank you!
– user7045242
Oct 21 at 0:12

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1 Answer
1

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secx=−1⟺cosx=−1⟺x≡πmod2π\sec x=-1\iff\cos x=-1\iff x\equiv \pi\mod2\pi.