Q: Find all solutions for X where 0 < X < 360 degrees and 9*cos(X) – 5 = 0.
Answer:
Okay, the 0 < X < 360 just tells you we are looking for answers in one complete circle (no more, no less).
So, we first need to solve for X like so:
9*cos(X) – 5 = 0
9*cos(X) = 5
cos(X) = 5/9
X = cos-1(5/9)
Plug this into your calculator and you get:
X = 56.25 degrees
This is part of your answer, but not all of it.
So, next, since, from our problem, we saw that:
cos(X) = 5/9
this means that the cosine value is positive. In what quadrants are the cosine values positive??
Quadrant 1 and Quadrant 4 have positive cosine values. Therefore, there will be 2 answers (one in each quadrant).
So, X = 56.25 degrees is the answer for the angle in Quadrant 1.
To get the angle in Quadrant 4 that also works, you gotta do 360 – 56.25 = 303.75
Therefore, 303.75 degrees is another answer for X.
What this is saying is that:
cos(56.25)= 5/9 and cos(303.75) = 5/9 also.
So, X = 56.25 and 303.75