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Derivatives Of Common Trigonometric Functions

I am taking Edexcel A-Level Maths.
In the formula booklet is a list of derivatives (and integrals) of common trigonometric functions. However, when putting this to the test, it has become clear that these lists are pretty incomplete.
I was wondering if anyone had a complete list of derivatives and integrals of common trig functions, that I can learn ahead of the exam? These are the one thing that hold differentiation and integration back from being really easy.
Thanks in advance!

Reply 1

Original post
by TobyAS
I am taking Edexcel A-Level Maths.
In the formula booklet is a list of derivatives (and integrals) of common trigonometric functions. However, when putting this to the test, it has become clear that these lists are pretty incomplete.
I was wondering if anyone had a complete list of derivatives and integrals of common trig functions, that I can learn ahead of the exam? These are the one thing that hold differentiation and integration back from being really easy.
Thanks in advance!

Why do you think the list is "incomplete"? There are only essentially 3 trig functions (sin / cos / tan), and in fact you could probably derive anything you wanted from sin alone, so there shouldn't be many "rules" that you need to learn!

Reply 2

Original post
by davros
Why do you think the list is "incomplete"? There are only essentially 3 trig functions (sin / cos / tan), and in fact you could probably derive anything you wanted from sin alone, so there shouldn't be many "rules" that you need to learn!

That is true, except it is far quicker and easier to answer these kinds of questions if you can spot the exact identity in the question. Especially with integration questions, where you are having to reverse the derivatives.
They are usually very low-mark questions, that just want you to apply the identity... if you're actually having to solve it in terms of sin and cos, then it becomes a much larger question.

Reply 3

Original post
by TobyAS
That is true, except it is far quicker and easier to answer these kinds of questions if you can spot the exact identity in the question. Especially with integration questions, where you are having to reverse the derivatives.
They are usually very low-mark questions, that just want you to apply the identity... if you're actually having to solve it in terms of sin and cos, then it becomes a much larger question.

https://www.drfrost.org/uploads/JFrost/files/C4CheatSheet.pdf
isnt bad, the last page has something like youre after. But as davros alludes to, Id practice deriving them rather than just memorising.

Reply 4

Original post
by TobyAS
That is true, except it is far quicker and easier to answer these kinds of questions if you can spot the exact identity in the question. Especially with integration questions, where you are having to reverse the derivatives.
They are usually very low-mark questions, that just want you to apply the identity... if you're actually having to solve it in terms of sin and cos, then it becomes a much larger question.

By solving the questions "properly" you probably learn the common results over time. It's not much more effort than memorising and lets you practise solving the real questions.

Reply 5

Original post
by TobyAS
That is true, except it is far quicker and easier to answer these kinds of questions if you can spot the exact identity in the question. Especially with integration questions, where you are having to reverse the derivatives.
They are usually very low-mark questions, that just want you to apply the identity... if you're actually having to solve it in terms of sin and cos, then it becomes a much larger question.

If you're relying on memorization then you're in danger of making a silly mistake in the exam if you mis-remember something!

Can you give an example of an integral (or derivative) where you think one of these "missing" formulae is going to make a big difference in speed?

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