Question

Find cosθ if sinθ = -12/13 and tanθ > 0.

Answer 1

A. -5/12
B. -5/13
C. 12/5
D. -13/12

Answer 2

cos theta = 1-sin^2theta = 1 - (-12/13)^2

Answer 3

costheta = \sqrt of the value u got

Answer 4

\[\cos(x) = \sqrt{1-\sin^2(x)}\]

Answer 5

How do I simplify that?

Answer 6

sin(x)=-12/13 => \[\sin^2(x) = 12^2/13^2\]

Answer 7

or you can use\[\sqrt{(1-\sin(x))(1+\sin(x))}\]

Answer 8

But I don't understand how to get one of the answers.

Answer 9

Where does the 5, 12, or 13 come in?

Answer 10

[1+(12/13)] [1-(12/13)] multiply

Answer 11

(25/13)(1/13)=(25/13^2)

Answer 12

1 - (12/13) + (12/13) - (12/13)^2

Answer 13

take the square root of that number

Answer 14

you will get :
\[\sqrt{\frac{ 5^2 }{13^2 }}\]

Answer 15

So 5/13?

Answer 16

yup

Answer 17

But is it -5/13? Because there is no positive 5/13.

Answer 18

yes its (-) because tan(x)>0

Answer 19

Okay, thank you so much!! You are a lifesaver. :)

Answer 20

\[\tan(x)=\frac{ \sin(x) }{ \cos(x) }\]

Answer 21

if sin(x)<0 then MUST BE cos(x)<0

Answer 22

Okay.

Answer 23

to make tan(x)>0

Answer 24

Oh, I get it now. Thank you so much!

Answer 25

any time