Question

How do you find the exact values of `sintheta` and `tantheta` when `costheta=0`?

Answer 1

`simtheta=+-1` and `tantheta` is not defined.

Explanation:

As `costheta=0`, we have

`sintheta=sqrt(1-cos^2theta)=sqrt(1-0)=sqrt1=+-1` and

`theta=+-pi/2`

But, `tantheta=sintheta/costheta` and as `sintheta!=0`, but `costheta=0`, `tantheta` is not defined.

However, as `theta->pi/2` from left (on real number line), `tantheta->oo` and as `theta->pi/2` from right (on real number line), `tantheta->-oo`.

Similarly, as `theta->-pi/2` from left (on real number line), `tantheta->oo` and as `theta->-pi/2` from right (on real number line), `tantheta->-oo`.
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