Question

I'm having trouble doing trigonometry.

Determine the possible coordinates of a terminal point for each angle in standard position.

A) 315°

I have no clue how to do this. Please explain and show me the work so I can do the rest of the questions myself

Answer 1

if the radi is 1, then
1@315=sin315+jcos315= -0.707+j.707

Answer 2

And if I choose 4 as the radi. Then would it be:
sin (315°)= y/4
4 sin (315°)= -2.8284
So that is the y value.

Cos (315°) = x/4
4 cos (315°) = 2.8284
So that is the x value

?

Answer 3

Where are you measuing the angle from, and in which direction? It makes all the difference. If you are measuring from the positive x axis, counterclockwise, yes, x will be positve, and y will be negative, as you did above
My example was measuring the angle from the j (y axis), clockwise.
You

Answer 4

In trig we consider the positive x-axis to have a direction of 0 degrees (or radians) and consider counterclockwise to be a positive rotation, so
East -- 0
North -- 90
West -- 180
South -- 270

So for a unit circle of radius 1, any point
(x,y) can be labelled (cosθ , sinθ)
so for your angle of 135 degrees, we could have (cos135, sin135)
or
(-sqrt(2)/2 , 1/2)

bobpursley gave you -0.707+j.707
which is the same thing expressed as a vector.

multiply the x and y coordinates by the same number would simply change the length of your radius.