Trig Identities: How to Ace Calc II Without Memorizing Every Identity

[ScienceMan]

I was wondering exactly what parts of trig I need to do to do well in Calc II. I took trig this past spring and aced it and I'm taking Calc I this semester. I'm not worried about this semester because I know my instructor won't use trig outside teaching us how to take the derivatives of the trig functions. But I know trig is used much more in Calc II. I'm not too worried since I did so well but I'm concerned about my ability to remember the sum/difference and double/half angle identities. I can figure out the Pythagorean identities from the equation sin²θ +cos²θ=1 and I'm fine with the graphs but I never really memorized the other identities because the professor I took let us write formulas on note cards for the tests.

Will my knowledge of trig be sufficient when I take Calc II in the spring?

 

[fresh_42]

It is like with everything you learn to memorize. Nowadays many things can easily and everywhere be looked up, so the need to memorize them is much less given than a few decades ago. And with a few identities (cosine and sine theorem and similar) and definitions (tangent and cotangent) they can also be derived in case they are needed. We used books with formulas of this kind, nowadays I take a quick view on Wikipedia. E.g. I know that the derivative of sine is cosine and vice versa, but I cannot remember the sign. But as I know their values and behavior at zero, I also know the sign of their derivatives. If you would be requested to know all trigonometric formulas, where does it end? Will you have to know their series expansions, too? Formulas, which are often used will automatically be memorized and the others can be looked up or derived. I think it's more important to concentrate on principles and concepts than on results. But in the end, this, too, is only an opinion which might not be shared by everyone.

 

[MidgetDwarf]

I was wondering exactly what parts of trig I need to do to do well in Calc II. I took trig this past spring and aced it and I'm taking Calc I this semester. I'm not worried about this semester because I know my instructor won't use trig outside teaching us how to take the derivatives of the trig functions. But I know trig is used much more in Calc II. I'm not too worried since I did so well but I'm concerned about my ability to remember the sum/difference and double/half angle identities. I can figure out the Pythagorean identities from the equation sin²θ +cos²θ=1 and I'm fine with the graphs but I never really memorized the other identities because the professor I took let us write formulas on note cards for the tests.

Will my knowledge of trig be sufficient when I take Calc II in the spring?

You need to understand Inverse functions, particularly inverse trigonometric functions, polar coordinates and their graphs, and the identities.

I can barely remember them myself, but I know how to derive them. Their is a near derivation that involves the use of 2 unit circles. From this you can get all the trigonometric identities. I recommend you google it.

For example, I can never remember cos(a)sin(b). But I know sin(a+b)=sin(a)cos(b)+cos(a)sin(b) and sin(a-b)=sin(a)cos(b)-cos(a)sin(b). Now, sin(a+b)-sin(a-b)=2cos(a)sin(b).
Now divide by 2 on both sides of the equation and woohoo we get that identity. It is not very hard.