What are the essential trig identities for solving calculus problems?

[PCSL]

I am currently taking Calc II and we are doing trig substitutions at the moment. I seem to have forgotten almost all the important trig identities. I understand that this sounds like something I should google but I honestly cannot find a good list of the trig identities I should know at this point. If someone could help me with the trig identities that I should memorize I would appreciate it. Thank you.

Edit: An example would be sin(2x)=2sin(x)cos(x) or tan²(x)=sec²(x)-1. Those are two I remember but I know I am forgetting a ton.

 

[rock.freak667]

http://www.sosmath.com/trig/Trig5/trig5/trig5.html"

Try to learn them when doing questions or else you'll be trying to learn a long list where you may struggle to see when to use it in a given question.

 

[PCSL]

http://www.sosmath.com/trig/Trig5/trig5/trig5.html"

Try to learn them when doing questions or else you'll be trying to learn a long list where you may struggle to see when to use it in a given question.

Thank you, that really helped.

 

[Ocasta]

I made flashcards, but I agree that you need to practice them with problems. Here are a few of mine:

$\sin ^2 x + \cos ^2 x = 1$

$1 - \sin ^2 x = \cos ^2 x$

$1 - \cos ^2 x = \sin ^2 x$

$\sec ^2 x - \tan ^2 x = 1$

$\sec ^2 x - 1 = \tan ^2 x$

$\sec ^2 x = 1 + \tan ^2 x$

$\csc ^2 x - \cot ^2 x = 1$

$1 + \cot ^2 x = \csc ^2 x$

$\csc ^2 x - 1 = \cot ^2 x$


I don't often run into the half angle identities, but they come up occasionally.

 

[gb7nash]

I made flashcards, but I agree that you need to practice them with problems. Here are a few of mine:

$\sin ^2 x + \cos ^2 x = 1$

$\sec ^2 x - \tan ^2 x = 1$

$\csc ^2 x - \cot ^2 x = 1$


I don't often run into the half angle identities, but they come up occasionally.

Here's a little trick, so that you don't need to rely on brute memorization. We want to memorize the following well-known identity:

$$sin^2 x + cos^2 x = 1$$

If you divide both sides by cos²x, you get:

$$tan^2 x + 1 = sec^2 x$$

which is the second identity rearranged. Similarly, if you divide both sides by sin²x, you get:

$$1+cot^2 x = csc^2 x$$

which is the third identity rearranged. I can't think of any other identities that can be derived like this, but this saves the effort of memorizing, or provides a sanity check to make sure that what you memorized is correct.

 

[Ocasta]

Here's a little trick, so that you don't need to rely on brute memorization.

...

this saves the effort of memorizing, or provides a sanity check to make sure that what you memorized is correct.

Agreed, my method was the memorize the big three and manipulate them.