# Trig Substitution Problem w/ tan substitution

• Burjam
In summary, the conversation involved discussing a problem involving trigonometric identities and a solution that was not yielding the correct answer. The person providing the solution was missing a square root in their formula for csc (theta) and did not understand the concept of Pythagoras' Theorem. After being reminded of the theorem, they realized their mistake and apologized for their error.
Burjam

Under #3

Trig identities

## The Attempt at a Solution

The picture attached is my attempt. The square in the upper upper left is the problem and the one in the lower right is my solution. I'm seeing that I'm getting the wrong answer, but not how.

You should type in the problem at least.
The formula for csc (theta) is wrong, You miss a square root.

fresh_42
I miss a square root? Where does a square root come into play? None of the sides of the triangle should have a square root in them.

Burjam said:
I miss a square root? Where does a square root come into play? None of the sides of the triangle should have a square root in them.
Really? So the dimension of the sides of a right triangle is length, but that of the hypotenuse is length-squared?
Recall Pythagoras' Theorem.

Haha sorry I did this while really tired... my bad.

## 1. What is trigonometric substitution?

Trigonometric substitution is a technique used to evaluate integrals involving algebraic expressions and trigonometric functions. It involves substituting trigonometric identities for algebraic expressions to simplify the integral.

## 2. What is a tan substitution?

Tan substitution is a specific type of trigonometric substitution where the variable is substituted with the tangent function and the resulting integral is evaluated using trigonometric identities.

## 3. How do I know when to use trigonometric substitution?

Trigonometric substitution is typically used when the integral involves a combination of algebraic expressions and trigonometric functions, and when u-substitution or other methods are not applicable.

## 4. What are the steps for solving a trig substitution problem with tan substitution?

The steps for solving a trig substitution problem with tan substitution are: 1) Identify the appropriate substitution by looking for a square root of an expression containing a variable, 2) Substitute the variable with the tangent function, 3) Rewrite the expression using trigonometric identities, 4) Evaluate the resulting integral, and 5) Substitute back the original variable to obtain the final answer.

## 5. Are there any common mistakes to avoid when using trigonometric substitution?

Some common mistakes to avoid when using trigonometric substitution include forgetting to substitute back the original variable, incorrect use of trigonometric identities, and not considering the appropriate substitution for the given integral.

Replies
4
Views
649
Replies
18
Views
3K
Replies
1
Views
1K
Replies
4
Views
1K
Replies
3
Views
1K
Replies
7
Views
2K
Replies
2
Views
1K
Replies
3
Views
1K
Replies
4
Views
2K
Replies
1
Views
1K