Solving Trigonomic Inequalites

[05holtel]

Find where cosθ = -0.8660, where (0 degrees ≤ θ < 540 degrees)

I am not sure how to solve this problem

I did: cosθ + 0.8660 = 0

Then I am not sure what to do

 

[HallsofIvy]

Well, use a calculator! That will give you the "principal value". Then use the fact that cosine is periodic with period 360 degrees and that cos(360- t)= cos(t) to find all other values.

 

[Nick89]

$$\cos \theta = -0.8660$$
$$\theta = \arccos -0.8660$$

That's as far as you can go if you want to stay exact. But you can calculate the answer using a calculator (there is probably something like 'cos^-1' key on it, that's the arccos key.)

However, if you've worked with trigonometry for some time you will find that you recognize some numbers. For example: 0.8660 looks like it's probably meant to be $$\frac{1}{2} \sqrt(3) = 0.866025404...$$

The arccos of -1/2 sqrt(3) however IS exact (try it on your calc!):

Note, this is only one answer. If you allow theta to be in the range you specified you get more answers!