Sine, Co-sine, and Tangent: SOHCAHTOA

Date: 03/28/99 at 19:28:47
From: Angie
Subject: Sine, co-sine, and tangent

I am having trouble figuring out what to use when you are solving a 
problem; sine, co-sine or tangent. I know that you use SOHCAHTOA but 
how is that suppose to help me?

Thank you, 
Angie K.
Lago Vista, TX

Date: 03/29/99 at 09:02:23
From: Doctor Rick
Subject: Re: Sine, co-sine, and tangent

Hi, Angie, welcome to Ask Dr. Math!

The basic problems of trigonometry involve 3 quantities of a right 
triangle: 2 sides and an angle. Look at where the sides are with 
respect to the angle. 

   Use SINE if one is the leg Opposite the angle 
   and the other is the Hypotenuse. (SOH)

   Use COSINE if one is the leg Adjacent to the angle 
   and the other is the Hypotenuse. (CAH)

   Use TANGENT if one is the Opposite leg 
   and the other is the Adjacent leg. (TOA)

Actually, in a right triangle, if you know one of the angles besides 
the right angle, you can find the other angle, too (what is it?).
Therefore you could use the cosine of the other angle instead of the 
sine of the given angle, for instance; they are equal. (In fact, 
COSINE means "SINE of the complement," which is what the other angle 
is. The same is true of the COTANGENT.)

Once you know which trig function to use, you will have an equation 
relating the 3 quantities, such as

         B
       /|
      / |
   c /  |
    /   | a     sin(A) = a/c
   /    |
  /_____|
 A   b   C

One of the 3 quantities will be an unknown; solve for it. For 
instance, if you know that angle A = 60 degrees and side a = 5 inches, 
then

  sin(60) = 5/c

        c = 5/sin(60)

There are many kinds of trigonometry problems, but this basic type of
problem is at the root of all of them. If you are having trouble with 
a particular kind of problem, give us an example. Show us what you 
think you are supposed to do to solve it; this will help us understand 
exactly what you need help with.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/