Question

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

Answer 1

Explanation:

The given equation is:

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

Taking the Left hand side of the above equation, we get

=
`\sqrt{1-cos^2{\theta}}`

=
`\sqrt{sin^2{\theta}}` (Because
`sin^2{\theta}+cos^2{\theta}=1`)

=
`{\pm}sin{\theta}`

Thus,
`\sqrt{1-cos^2{\theta}}=-sin{\theta}` is true.

Now, since
`sin{\theta}` is negative, therefore it terminates in the third and the fourth quadrant because in third and fourth quadrant,
`sin{\theta}` is negative.

Answer 2

Yes it is true because:
(1 - cos^2 x) = sin^2 x Sqr.(1 - cos^2 x) = sin x and (-sinx) True, since sin x negative. Also, x terminates in quadrant 3 and 4. Hope this is helpful