Question

If `tantheta = sqrt(3)`, then how would you find the value of `sintheta`?

Answer 1

`sintheta = sqrt(3)/2`

Explanation:

We know that `tan^2theta + 1 = sec^2theta`, thus:

`sec^2theta = (sqrt(3))^2 + 1 = 4`

Thus `sectheta = 2`, and since secant is the reciprocal of cosine, `costheta = 1/2`.

We know that `tantheta = sintheta/costheta`, thus `sintheta = tanthetacostheta`.

`sintheta = 1/2(sqrt(3)) = sqrt(3)/2`

Hopefully this helps!