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

In summary, you need to understand inverse trigonometric functions, polar coordinates and their graphs, and the identities.
  • #1
ScienceMan
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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?
 
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  • #2
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.
 
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  • #3
ScienceMan said:
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.
 

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

1. What are the basic trigonometric identities that we need to know in Calculus II?

In Calculus II, we commonly use the basic trigonometric identities such as sine, cosine, tangent, cotangent, secant, and cosecant. These identities are useful in simplifying complex trigonometric expressions and solving integrals.

2. How do we prove trigonometric identities in Calculus II?

To prove a trigonometric identity, we use various algebraic techniques such as factoring, expanding, and substitution. We also use the properties of trigonometric functions, such as the Pythagorean identities, to simplify the expressions and show that they are equivalent.

3. What is the difference between sum and difference identities in Calculus II?

The sum identities are used to find the trigonometric function of the sum of two angles, while the difference identities are used to find the trigonometric function of the difference of two angles. Sum identities include the double angle formulas, while the difference identities include the half angle formulas.

4. How do we use trigonometric identities in solving integrals?

Trigonometric identities are used in solving integrals by simplifying the integrand into a form that can be easily integrated. This is particularly useful when we have trigonometric functions raised to powers or when the integrand contains multiple trigonometric functions.

5. Are there any common mistakes to avoid when using trigonometric identities in Calculus II?

One common mistake to avoid is using the wrong trigonometric identity or misapplying the correct one. It is important to carefully match the given expression with the correct identity and to also make sure that any substitutions or simplifications are done correctly. Additionally, it is important to be familiar with the basic trigonometric identities and their corresponding graphs to avoid errors in calculations.

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