Basic Trig Identities
Next let's see how these functions are related. These are identities
you will need for calculus (there are many others you learned in
your trig class that we generally do not use in calculus).
 $\sin(\theta)=\sin(\theta)$
 $\cos(\theta)=+\cos(\theta)$
 $\sin(2\theta)=2\sin(\theta)\cos(\theta)$
 $\sin^2(\theta)+\cos^2(\theta)=1$
 $\tan^2(\theta)+1=\sec^2(\theta)$
 $1+\cot^2(\theta)=\csc^2(\theta)$
 $\cos^2(\theta)=\frac{1+\cos(2\theta)}{2}$
 $\sin^2(\theta)=\frac{1\cos(2\theta)}{2}$

The first two say that sine is an odd function, and that cosine
is an even function.
DO: Play with positive
and negative angles on the unit circle to see why the first two
identities make sense.
The next three are called Pythagorean
identities, since they're all based on the
Pythagorean theorem. Notice that if you take the primary
Pythagorean identity, $\sin^2(\theta)+\cos^2(\theta)=1$, and
divide all terms by $\cos^2(\theta)$ you get the tangent/secant
Pythagorean identity. Similarly, if you divide all terms of
the primary identity by $\cos^2(\theta)$ you get the
cotangent/cosecant identity. You need not memorize the last
two since they are so easily computed.
The last two identities will be used to help compute integrals,
during the second semester of calculus.
