Integrating Monomials

You've already learned what sines and cosines are. Now we're going to learn 4 new trig functions! No, there's nothing to fear about them, after all, they can each be expressed in terms of sines and cosines. Let's learn the names first: tangent, cotangent, secant, and cosecant. Tangent. Cotangent. Secant. Cosecant. What are they? Okay, seems like you've got it. Now let's learn their meanings.

Tangent: To write the tangent of an angle $\theta$, we write it as $\tan(\theta)$. $\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$. Got it? Great, let's move on.

Cotangent: To write the cotangent of an angle $\theta$, we write it as $\cot(\theta)$. Cotangent is simply the reciprocal of tangent, so what do you think it is in terms of sines and cosines? Yep, you're right: $\cot(\theta)=\frac{\cos(\theta)}{\sin(\theta)}$.

Secant: To write the secant of an angle $\theta$, we write it as $\sec(\theta)$. This one is slightly harder as it is no longer a reciprocal, but you're great at trig, I know you can do it! $\sec(\theta)=\frac{1}{\cos(\theta)}$. Yep, just $\tan(\theta)$ with a 1 instead of a $\sin(\theta)$. Understand? There's just one more!

Cosecant: To write the cosecant of an angle $\theta$, we write it as $\csc(\theta)$. Cosecant is the sine version of secant, so what do you think it is in terms of sines and cosines? Wonderful: $\csc(\theta)=\frac{1}{\sin(\theta)}$.

I hope you have enjoyed learning the other 4 trig functions. You're awesome. Now here's a worksheet so that you can practice your newly acquired skills: http://www.chino.k12.ca.us/site/handlers/filedownload.ashx? Good luck!