Trig identities?

Question

I know how to solve some identities, but overall I have a hard time on solving them. I don't want an answer relating to a specific problem, but any tips or tricks on how to start solving any type of problem using any of the six functions. I have a test in a few days and we have a limited amount of time to solve the problems so I don't want to just try different things randomly until one works.

Answer 1

Try several things. It usually helps to put everything into sines and cosines. You can also work both sides, then go back and work from just one when you see how they become equal. Of course, you must know your basic identities first.

Answer 2

If you can handle the messy looking algebra it helps to restate the problem in its original definitions. Instead of just righting for example sinx put in y/r or opposite / hypotenuse (depending on the problem you must chose which way to state the definition, it will change). It often helps to sketch the triangles showing the relations and to sketch the trig function curves. The sketches do not have to be all that accurate.

As some identities get fairly involved you can often start eliminating a lot of the terms by simplification.

AT the start I said messy looking algebra. It is not really messy, often opening up one side or the other or both is the only way to get started.

Answer 3

in your seat a few days ago. I found copying problems at the back of the book , about a hundred of em or so. helped me see the different combinations and gave me a nice understanding. Althought my answers at the back of the book gave step by step examples. I attempted to do the problems but kept looking at the answers. I then decided to write out the steps and answers. This helped me remember the different combos good luck. BTW Itll get easier. Dont give up!

Answer 4

One secret is to multiply both sides of the identity by e^x. Since e^x cannot be differentiated, this lends a notion of stability to the equation. Having done this, it is a simple matter to solve for the value of x by substituting into the equation e^e = e.

Answer 5

If one side of the identity is more comlicated than the other, then start with the more complicated side.

Good identities to remeber are
sin (2x) = 2sinxcosx
cos (2x) = cos^2(x) - sin^2(x)
cos(2x) = 1 - sin^2 (x)
cos(2x) = 2cos^2(x) -1
tan (2x) = 2tan (x)/(1-tan^2(x)
sin(x) + sin(y) = 2sin.5(x+y)cos.5(x-y)
cos(x) + cos(y) = 2cos.5(x+y).cos.5(x-y)
a cos(x) +bsin(x) =cos (x-y), where c =sqrt(a^2+b^2)
a cos(x) +bsin(x) = csin(x-y), y = arctan (b/a)