Corresponding values of a giving trig function

[lorenzarthur]

Hey guys!
I have to solve the task "find the corresponding cos-value for sin(x)=3/5. My textbook only gives the positive solution of cos(x)=4/5. But if the angle x happens to be obtuse, I should get -4/5 as an answer as well, right? Given that I don't now the size of x, I should state both solutions, unless talking specifically about a given triangle, correct?
I'm especially confused, because for the similar task of finding the sin(x) for tan(x)=2, there are two solutions given (+/- 2/sqroot5).
Thanks in advance!

 

[Steven G]

I think that your logic with there being two answers is correct.

 

[MarkFL]

Hello, and welcome to FMH!

I edited your post to remove links to youtube channels/videos. They aren't needed for the problem, and this site isn't meant to be a platform on which to promote such things.

To answer your question, if we are told:

[MATH]\sin(x)=\frac{3}{5}[/MATH]
Then you would be correct (with no restrictions given on \(x\)) to then state:

[MATH]\cos(x)=\pm\frac{4}{5}[/MATH]

 

[lorenzarthur]

Hello, and welcome to FMH!

I edited your post to remove links to youtube channels/videos. They aren't needed for the problem, and this site isn't meant to be a platform on which to promote such things.

To answer your question, if we are told:

[MATH]\sin(x)=\frac{3}{5}[/MATH]
Then you would be correct (with no restrictions given on \(x\)) to then state:

[MATH]\cos(x)=\pm\frac{4}{5}[/MATH]

Thanks a lot for the fast help Mark! Sorry, wasn't aware of the link (I had originally posted this as a comment to a trigonometry-video on yt, and didn't notice there was a link created when copying).

 

[Dr.Peterson]

Hey guys!
I have to solve the task "find the corresponding cos-value for sin(x)=3/5. My textbook only gives the positive solution of cos(x)=4/5. But if the angle x happens to be obtuse, I should get -4/5 as an answer as well, right? Given that I don't now the size of x, I should state both solutions, unless talking specifically about a given triangle, correct?
I'm especially confused, because for the similar task of finding the sin(x) for tan(x)=2, there are two solutions given (+/- 2/sqroot5).
Thanks in advance!

What was the context of the problem in your textbook? I don't suppose it was in a section on acute angles, where trig functions of other angles have not yet been introduced, with the tangent problem in a later section? Or was something said in the instructions to this, or a set of problems, that would restrict the angles in view? Or did you not quote the exact words of the problem?

It is odd that they would give two answers for one problem but not for the other, if both problems were worded identically.

 

[lorenzarthur]

The problem was given after a longer explanation of the all the trig-basics, beginning with acute angles in triangles, but then extending the concept to all quadrants in the unity circle. The two problems were stated together, as sub-prolems 1a) and 1b). So no restricion to the angle was expected. I'm learning alone with a textbook, so I thought I may have not "gotten" something important...