Question

Find a value of θ in the given interval.
cosθ= 0.458 [270, 360]

Answer 1

would you know how to solve cos(p)=1/2 between 270 and 360?

Answer 2

On the unit circle, it is obvious that p would have to be 300 degrees.
We could get this same answer by doing the following process:

p=arccos(1/2)
but this p will give us 60 degrees instead of something between 270 and 360

so
we know that cos is an even function
therefore arccos is also

so

we could say cos(p)=1/2 implies we have the other solution p=arccos(-1/2)
but this would give us something between 90 and 180
so if we want to follow a straight line down to the 4th quadrant where we have a positive
value then we would need to do p=arccos(-1/2)+180
this would mean p=120+180=300 just like we got using unit circle

Answer 3

Yeah, I understand how to do it when it's a simple value, but don't understand how to do it when its a random decimal like .458

Answer 4

@jbird17 I explained my answer with and without using the unit circle values

Answer 5

actually almost gave you the answer
your equation cos(p)=.458 is totally similar to my equation cos(p)=1/2
replace the 1/2 with .458