Thread: Trigionometric ratios

I am working on a problem with a 3 4 5 right triangle and it asks for the given angle x in the triangle given in the graph find
sin x=
cos x=
tan x=
cot x=
sec x=
csc x=
I thought sin= opp/hyp or in this case 3/5, I thought I understood what the book was saying but the answer in the back of the book did not match. Please, if you have time, help me to understand this concept.

Thank you very much!!!!!!!!!!!!
Keith Stevens
keithstevens@ctc.net

Originally Posted by kcsteven

I thought sin= opp/hyp. I understood what the book was saying but the answer in the back of the book did not match. Please, if you have time, help me to understand this concept.

Looks like you understand it to me -- I just did this exact same thing again in a review. What does the book say the right answer is? The only thing that I can think of is that you are not oriented correctly. I really need more information to help you: There are three angles in a 3 4 5 right triangle, and you could label any of them x; the answers will be different depending on which angle you are taking the trig functions of. Can you draw the triangle? Even a sketch in a paint program would be helpful -- it is not as important that it be perfectly accurate as that it be labeled exactly the way it is in the assignment.

EDIT: look below for my post. i screwed this one up

It depends on how your triangle is set up. The lengths of the sides form a Pythangorean triple since it has sides of 3,4,5. If the answer is not 3/5, I'm assuming it's 4/5. So I'm guessing this is how your triangle is set up.

Code:

                     --
                     -   -
                     - 30  -
                     -         -
                  4  -            -     5
                     -               -
                     -                  -
                     - 90            x   -
                     ------------------   
                                3

sin(x) = opp/hyp = 4/5
cos(x) = adj/hyp = 3/5
tan(x) = opp/adj = 4/3

cot(x) is the reciprocal of tan(x). Since tan(x) = 4/3, cot(x) = 3/4
sec(x) is the reciprocal of cos(x). Since cos(x) = 3/5, sec(x) = 5/3
csc(x) is the reciprocal of sin(x). Since sin(x) = 4/5, csc(x) = 5/4

Sorry for the horrible triangle