Finding the x and y components of a vector

Question

Find the x and y components of vector with a magnitude of 8 and 130° with the horizontal, respectively.

Answer 1

A picture could look like this:

You can see that a right triangle is formed with an angle of 50° meaning you could write a trig ratio using sine and cosine for that angle as follows:

sin(50°) = opposite/hypotenuse = y-component/8

cos(50°) = adjacent/hypotenuse = x-component/8

Rearranging these (solving for the y-component and the x-component) we get:

y-component = 8sin(50°) = 6.128

x-component = 8cos(50°) = 5.142 but since the x-component is in the negative x-direction, it should probably be answered as -5.142