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

Mar 4, 2017

$x = \pm 4$

Explanation:

By the definition of sine, we have

$\sin \theta = \text{opposite"/"hypotenuse} = - \frac{3}{5}$

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:

${5}^{2} - {\left(- 3\right)}^{2} = {a}^{2}$ where $a$ is the side adjacent $\theta$

$25 - 9 = {a}^{2}$

$a = \sqrt{16}$

$a = \pm 4$

The side opposite $\theta$ is always the $y$-value, while the side adjacent $\theta$ is always the $x$-value. Therefore, $x = \pm 4$.

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!