SinĀ Īø =Ā
First we need to think, where isĀ Īø?Ā
BecauseĀ Īø is the same as a variable so it will be the same for cosĀ Īø.Ā
They didn't give us an intervalĀ to work with so there will be multiple answers.
First we need to find when sinĀ Īø is positive.Ā
Imagine (or create) the unit circle. It's within a x and y plane. So the two quadrants where y is positive is the 1stĀ and 2nd quadrant.
Try to devote the angles on the unit circle to memory, it helps a lot!Ā
sinĀ Īø =Ā
Needs a reference angle ofĀ
Or in the case of the 1st quadrant it is that angle.Ā
So, we have one angle of the two.
TakeĀ
and subtract
from it. (Don't use a calculator!)
Is the number you should get.Ā
So we have the two possible angles. Now to find the cos of those angles. Pro tip! When sin Īø =Ā
cos Īø =Ā
Where + / - is the symbol plus or minus. Whether it is one or the other depends on the quadrant is resides in.Ā
We have two answers! One that will be positive (quadrant 1) and one that will be negative (quadrant 2)
Those are our two answers. Hope this helps!Ā