Question

How do you find x if the point (x,-3) is on the terminal side of theta and `sintheta=-3/5`?

Answer 1

`x = +- 4`

Explanation:

By the definition of sine, we have

`sintheta = "opposite"/"hypotenuse" = -3/5`

Therefore, the side opposite `theta` measures `-3` units and the hypotenuse measures `5` units. These can be seen as dimensions on a right angled triangle, so we have, by pythagoras:

`5^2 - (-3)^2 = a^2` where `a` is the side adjacent `theta`

`25 - 9 = a^2`

`a = sqrt(16)`

`a = +- 4`

The side opposite `theta` is always the `y`-value, while the side adjacent `theta` is always the `x`-value. Therefore, `x = +- 4`.

We can't specify whether it is `x = +4` or `x= -4` unless you give us the quadrant (e.g. Quadrant III, or Quadrant IV).

Hopefully this helps!