17Calculus Precalculus - Trig Identities

17Calculus

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

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.