Trig. Question

  • Thread starter kg90
  • Start date
  • #1
3
0
sin-1(-1/2)


Can someone explain how to do this problem by hand. Thanks.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
Welcome to PF!

sin-1(-1/2)


Can someone explain how to do this problem by hand. Thanks.

Hi kg90! Welcome to PF! :smile:

May I check … do you know how to do sin-1(1/2)?
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
964
What is your definition of sine? (Since a right triangle cannot have an angle whose sine is -1/2, I assume you are NOT using "opposite side divided by hypotenuse" as your definition.
 
  • #4
3
0
Hey thanks for replying. I do know how to do most problems like this. I just don't know how you get the negative answer for the problem I posted above. I always end up with a positive.

HallsofIvy, I'm not sure..
 
  • #5
623
0
Think about which quadrant you are working in and where sine, cosine, etc. are positive/negative?
 
  • #6
3
0
Think about which quadrant you are working in and where sine, cosine, etc. are positive/negative?

Yeah, but aren't there two quadrants where that would be true?
 
  • #7
623
0
Yes, and therefore on the interval [0, 2pi), there will be 2 answers.
 
  • #8
623
0
Think about it this way, you probably know or can convince yourself (and if you can't, try to) that f(x) = sin(x) crosses the x - axis twice on the interval [0, 2pi) (which points would that be?). Now how would you do that? Well you would say f(x) = sin(x) = 0, so I need to find x such that x = sin^{-1)(0). Now in your case you have g(x) = sin(x) - 1/2 and you are trying to find those x-intercepts, so you solve g(x) = sin(x) - 1/2 = 0 or in other words x = sin^{-1}(1/2).
 
  • #9
tiny-tim
Science Advisor
Homework Helper
25,832
251
Hey thanks for replying. I do know how to do most problems like this. I just don't know how you get the negative answer for the problem I posted above. I always end up with a positive.
Yes, and therefore on the interval [0, 2pi), there will be 2 answers.

Hi kg90! :smile:

(have a pi: π :smile:)

"sin-1" normally means the principal value of sin-1

that's the one in (-π/2,π/2] …

in other words, nearest to 0. :smile:

it may help to think of the sin as the y coordinate of the angle …
so sin-1(-1/2) is the angle where the y coordinate is -1/2 :wink:
 

Related Threads on Trig. Question

  • Last Post
Replies
2
Views
533
  • Last Post
Replies
2
Views
980
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
2
Replies
33
Views
3K
  • Last Post
Replies
23
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
1K
Top