• Support PF! Buy your school textbooks, materials and every day products Here!

Solving Trigonomic Inequalites

  • Thread starter 05holtel
  • Start date
  • #1
52
0
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
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,770
911
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.
 
  • #3
555
0
[tex]\cos \theta = -0.8660[/tex]
[tex]\theta = \arccos -0.8660[/tex]

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 [tex]\frac{1}{2} \sqrt(3) = 0.866025404...[/tex]

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!
 

Related Threads for: Solving Trigonomic Inequalites

Replies
4
Views
2K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
4
Views
1K
Replies
20
Views
2K
Replies
2
Views
611
Top