# Write an expression for tan in terms of sin and cos functions

The more important identities. Let's do one more example.

### Write each expression in terms of sines and or cosines and then simplify

Well the one thing that we do know-- and this is the most fundamental trig identity, this comes straight out of the unit circle-- is that cosine squared theta plus sine squared theta is equal to 1. The mnemonic "all science teachers are crazy" lists the functions which are positive from quadrants I to IV. So let's see. Well you might be tempted, especially with the way I wrote the colors, to think, hey, is there some identity for 1 plus sine squared theta? Pythagorean identity trig Video transcript Let's do some examples simplifying trigonometric expressions. We could either replace this 1 minus sine squared theta with the cosine squared theta, or we could replace this cosine squared theta with the 1 minus sine squared theta. For this purpose, any angular unit is convenient, and angles are most commonly measured in degrees. These are used in calculus for a particular kind of substitution in integrals sometimes called the Weierstrass t-substitution. Let's say that we have cosine squared theta plus 1 minus-- actually, let's make it this way-- plus 1 plus sine squared theta. You can easily reconstruct these from the addition and double angle formulas. Well we already know that 1 minus sine squared theta is the same thing as cosine squared theta. So if I can replace this with the cosine squared theta, then I think I'm simplifying this.

Identities expressing trig functions in terms of their supplements. These are used in calculus for a particular kind of substitution in integrals sometimes called the Weierstrass t-substitution.

For this purpose, any angular unit is convenient, and angles are most commonly measured in degrees. Periodicity of trig functions.

So how could I simplify this? A great advantage of radians is that many formulas are much simpler when using them, typically all formulas relative to derivatives and integrals. You should know that there are these identities, but they are not as important as those mentioned above.

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