Question

find cos x if sin^2 x - 1/cos x = -1

Answer 1

is that supposed to be

sin^2x - 1
--------- = -1
cos x

?

Answer 2

yessir

Answer 3

would have been better to write it as (sin^2 x - 1)/cos x = -1

what you wrote is actually

sin^2 x - (1/cos x) = -1

by the order of operator precedence (multiplication and division happen before addition and subtraction)

Answer 4

sorry about that! i didn't bother to use parenthesis because i didn't realize that it'd be different without them.

Answer 5

If sin^2 x + cos^2 x = 1, then

sin^2 x + cos^2 x - 1 = 0
sin^2 x - 1 = -cos^2 x

does that give you any ideas?

Answer 6

unfortunately not.

Answer 7

you must be getting tired, too :-)

sin^2 x - 1 = -cos^2 x

your problem is

(sin^2 x - 1) / cos x = -1

so we can write that as

(-cos^2 x) / cos x = -1

now we can cancel common factors on the left, leaving us with

-cos x = -1
cos x = 1

can you solve that?

Answer 8

remember, cos^2 x is just cos x * cos x
so we had

-cos x * cos x
------------ = -1
cos x

Answer 9

I do so wish that OpenStudy would fix the blinketyblank equation formatting!

Answer 10

cosine of 0 is 1, so the answer is 0?

Answer 11

let's try it out!

we think x = 0 might be the answer. let's plug it into the original and see if it works

sin x = sin 0 = 0

sin^2 0 = 0*0 = 0
sin^2 0 - 1 = 0 - 1 = -1
cos 0 = 1
-1/cos 0 = -1 / 1 = -1
-1 = -1
looks like it is a valid solution!

Answer 12

perfect! thank you so much for your help tonight.

Answer 13

you betcha! good night...