Question

find all the solutions to cos theta =1/2.

Answer 1

I think \(\large \mathbb {cos~\theta =\frac{1}{2}}\rightarrow \theta =cos^{-1}(\frac{1}{2})=\pm \frac{\pi}{3}+k2\pi\)

Answer 2

cos can only positive in the 1st and 4th so take the inverse for cos to get the angle
this would for the 1st

Answer 3

are there 2 solutions?

Answer 4

Are the solutions in any interval?

Answer 5

yes

Answer 6

[0,360)

Answer 7

Yes, as AJ01 said, the angles will be in 1st and 4th quadrant.

Answer 8

first angle =60
second = 360-60=300

Answer 9

good thats what i got! {60,300} is how I would write the answer correct?

Answer 10

Yes, that's how we write the solution set.

Answer 11

thanks!