# Differentiating Trig Functions again

• QuarkCharmer
In summary, the conversation discusses the process of simplifying and when to know when to stop. It is advised to stop simplifying when there are no obvious ways to continue, and the level of simplification needed may vary depending on the purpose of the problem. An example is mentioned where the simplification was not obvious but it was still considered sufficient.
QuarkCharmer

## Homework Statement

Does this look correct? How do I know when to stop simplifying things? Sometimes it comes out to a nice little expression, and other times it's a long solution. In the latter, I spend too much time trying to simplify it further!

## The Attempt at a Solution

Hi QuarkCharmer!

That looks ok!

About the simplifying. I think your simplification is quite good here. As soon as you don't see any way to simplify further, you're done. How much you want to simplify is quite dependent of what you want to do next. Sometimes, you don't need to simplify at all!

Thanks.

We were showed a simple example, where the derivative simplified down to something that COULD have been simplified further (but it wasn't obvious), and we were told that is where we should stop. I'm just confused as to what is expected ugh.

Can you maybe post this example? I don't see a good reason why you should stop simplifying. Unless they mean that the simplification is not easy, and that they don't want you to waste time on it...

## 1. What are the basic trigonometric functions?

The basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

## 2. How do you differentiate trigonometric functions?

To differentiate a trigonometric function, you can use the basic rules of differentiation such as the power rule, product rule, and chain rule. You can also use the trigonometric identities and the quotient rule if necessary.

## 3. What is the derivative of sine?

The derivative of sine is cosine (cos).

## 4. Can you differentiate inverse trigonometric functions?

Yes, you can differentiate inverse trigonometric functions using the inverse function rule.

## 5. What is the purpose of differentiating trigonometric functions?

Differentiating trigonometric functions helps us find the rate of change or slope of a curve at any given point. It is also useful in solving real-world problems involving trigonometric functions, such as in physics and engineering.

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