Question

Given `sin theta=3/5` and `cos theta=4/5`, how do you find `tan theta`?

Answer 1

`tan theta = 3/4`

Explanation:

Recall the quotient identity `tanx = sinx/cosx`

`tantheta = sinx/cosx`

`tantheta = (3/5)/(4/5)`

`tantheta = 3/5 xx 5/4`

`tantheta = 3/4`

Note you could have also said that

`sintheta = "opposite"/"hypotenuse"`, `costheta = "adjacent"/"hypotenuse"` and `tantheta = "opposite"/"adjacent"`.

If we know that `sintheta = 3/5`, the side opposite `theta` measures 3.

If we know that `costheta = 4/5`, the side adjacent `theta` metres 4.

Applying the definition of `tantheta = "opposite"/"adjacent"`, we have that `tantheta = 3/4`

Hopefully this helps!