Trigonometric identities plus#

So that's what we mean by simplifying a trigonometric expression.Дon't forget. So this whole big expression reduces down to the simple cosecant theta. I still have the operation of division and I can get rid of that if I just replace this with cosecant theta. Now when you're simplifying a trigonometric expression or any expression, it's best to have as few operations and as few functions in your final answer as possible.

Trigonometric identities plus#

And this is really good because notice, I can factor a sine theta out of the bottom and I'm left with cosine theta plus 1 which is exactly what I have in the numerator. Cosine times sine is sine cosine and sine over cosine times cosine the cosine's cancel and you get sine. So in the numerator, I get cosine times 1 over cosine is 1. Now remember when I do this, this cosine theta is going to be multiplied across both of these terms and this cosine theta will be multiplied across both of these terms. Notice that I have a complex fraction here and the denominators in the little fractions are cosine theta so I can get rid of them by multiplying the top and bottom by cosine theta. Now, at first glance, this is actually a little more complicated looking than we started but now that we've got sines and cosines we can simplify this using Algebra. And I'll replace tangent theta with sine theta over cosine theta. I'll replace secant theta with 1 over cosine theta. Secant theta plus 1, sine theta plus tangent theta.ДЄ lot of times when you're dealing with um some of the reciprocal trig functions, the best strategy is to switch to sines and cosines. So let's use that to simplify secant theta plus 1 over sine theta plus tangent theta. Secant theta equals 1 over cosine theta, cosecant theta is 1 over sine theta and tangent theta is sine theta over cosine theta. These are some of the reciprocal identities. Well let's recall some basic trig identities that will be need right now. One of the things that you'll find in your homework occasionally is problems that ask you to simplify a trig expression. Trigonometric identities are really important as you've probably already seen if you've used them to graph.