Answer:
t = -35 + 360n where n is any integer
Step-by-step explanation:
I assume o is theta. I am going to use t for theta.
sin(55) = cos(t)
The easiest way is to know that one graph is a vertical shift of the other. so sine starts at 0 while cosine starts at 1 and doesn't get to 0 until you are at an input of 45 (or pi/2 degrees). so sin(x) = cos(x - 90) = cos(x + 270) and cos(x) = sin(x + 90) = sin(x - 270). ALSO keep in mind you can add/ subtract an additional 360 since that cycles the graph again
Anyway, that is what you can use.
sin(55) = cos(t) = cos(55 - 90)
t = 55 - 90
t = -35
then again, remembering you can subtract a further 360 to get the same number the expression that is the answer is t = -35 + 360n where n is any integer
