Question

If sin Θ = 7 over 25, use the Pythagorean Identity to find cos Θ.

Answer 1

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

Answer 2

@alikat641

Answer 3

How did you get that? Because i only have notes that say \[\sin^2\theta=1-\cos^2\theta\] \[\cos^2\theta=1-\sin^2\theta\] and \[\sin^2\theta+\cos^2\theta=1\]

Answer 4

check the second equation.. Take square root on both sides... If the range of theta is not given, put a +/- sign in the expression i gave

Answer 5

@alikat641

Answer 6

Hi... @alikat641

Answer 7

oh sorry i was taking care of something. so how do i plug in the original equation? It's not squared.... do i just square both sides and plug it in?

Answer 8

\[\cos \theta=\sqrt{1-(\frac{ 7 }{ 25 }})^2\]

I think i did that right. and ignore my previous question, I didn't see the parentheses

Answer 9

yeah correct/// Now just evaluate the value

Answer 10

\[\cos \theta=\sqrt{1-\frac{ 49 }{ 625 }}\] \[\frac{ 1 }{ 1 } - \frac{ 49 }{ 625 }\]\[\cos \theta=\sqrt{\frac{ 576 }{625 }}\]

Answer 11

so i square root the whole fraction or do i individually square the numerator and then the denominator?

Answer 12

576=24^2 and 625=25^2 so it reduces to 24/25

Answer 13

@alikat641

Answer 14

so \[\cos \theta=\frac{ 24 }{ 25 }?\]

Answer 15

yeah, write +24/25 and -24/25, since we dont know the range of theta

Answer 16

\[\pm \frac{ 24 }{ 25 }\]

Answer 17

gotcha. thanks a ton :D

Answer 18

correct.:)