Question

Is square root 1 minus sine squared theta = cos Θ true? If so, in which quadrants does angle Θ terminate?

Answer 1

@One098

Answer 2

remember that \(cos^2(\theta) + sin^2(\theta) = 1\), so \(cos^2(\theta)=1-sin^2(\theta)\)

Answer 3

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

Answer 4

so then \[\cos(\theta) =\sqrt{\cos ^{2}(\theta)+\sin ^{2}(\theta)-\sin ^{2}(\theta)}\]

Answer 5

\[\sqrt{\cos^2(\theta)}=\cos(\theta) \text{ if } \cos(\theta)>0 \\ \sqrt{\cos^2(\theta)}=-\cos(\theta) \text{ if } \cos(\theta)<0\]

Answer 6

yeah... but why you would write like this?

Answer 7

yes @freckles is correct

Answer 8

the two sins cancel out, so its just \[\cos (\theta)=\sqrt{\cos ^{2}(\theta)}\]

Answer 9

I write like that to make it eaiser to see

Answer 10

\(cos(\theta)\) is negative in the second and third quadrants

Answer 11

I can tell its true because its squared and has a square root, and then assuming "terminate" means negative, which makes you right