Question

Is `sqrt(1-cos^2 theta) = -sintheta` true?

Answer 1

Sometimes

Explanation:

It helps to know some Pythagorean identities:

If we solve for the first one, we can see that `sin^2x=1-cos^2x`. Substitute this inside the square root. Note that `x` is just a dummy variable, we could use `theta` instead:

`sqrt(sin^2theta)=-sintheta`

Simplify the left side:

`+-sintheta=-sintheta`

Since `sintheta` is an odd function, we can only conclude that `-sintheta=-sintheta`, and as such, `sqrt(1-cos^2x)=-sintheta` when `theta` is negative, for example.