# sec (theta) = -5?

Solve for 0 <= (theta) < 360 :

sec (theta) = -5

[ In degrees ] Calculator okay.

Thanks for any help you can offer ^^

### 4 Answers

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- PuggyLv 71 decade agoFavorite Answer
sec(t) = -5

First, let's express this as cosine. Note that sec(t) = 1/cos(t), so

1/cos(t) = -5. Take the reciprocal of both sides, and we get

cos(t) = -1/5

-1/5 isn't any of our known values on the unit circle. For that reason,

t = arccos(-1/5)

This is one of our values, and it is in the second quadrant. We should have another value in our third quadrant. Our other solution would be 360 - arccos(-1/5), so

t = {arccos(-1/5), 360 - arccos(-1/5)}

Our approximate values are

t ~= {101.54, 258.46}

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- 1 decade ago
i will use x instead of theta:

sec x = -5

1 / cosx = -5 [now take recipriocals]

cos x = -0.2

x = 101.5, 258.5

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