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17Calculus Precalculus - Trig Identities

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Trig Identities

Here is a list of the trig identities you will use most in calculus.

Set 1 - Basic Identities

\(\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }\)

\(\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }\)

\(\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }\)

\(\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }\)

Set 2 - Squared Identities

\( \sin^2t + \cos^2t = 1\)

\( 1 + \tan^2t = \sec^2t\)

\( 1 + \cot^2t = \csc^2t\)

Set 3 - Double-Angle Formulas

\( \sin(2t) = 2\sin(t)\cos(t)\)

\(\cos(2t) = \cos^2(t) - \sin^2(t)\)

Set 4 - Half-Angle Formulas

\(\displaystyle{ \sin^2(t) = \frac{1-\cos(2t)}{2} }\)

\(\displaystyle{ \cos^2(t) = \frac{1+\cos(2t)}{2} }\)

Remembering trig identities can be difficult. However, there are techniques to help you learn and memorize them. The main way to remember anything is to use it. It also helps to see how other people remember them. Here are some videos where the instructor explains how he remembers them. You may be able to pick up some techniques and new ideas from these videos.

Trig Identities - Derive and Remember

Okay, so these identities may be a bit overwhelming to learn and remember. Here is a fun video that shows the geometric interpretation of all 6 trig functions. He goes through them pretty fast, so you may want to take notes but this gives you another way to remember the trig identities.

3Blue1Brown - Tattoos on Math [8min-14secs]

video by 3Blue1Brown

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