# Homework Help: Component Identities

1. Oct 4, 2005

### brandon26

Solve for x

3sin(x+10)=4cos(x-10)

I tried changinf everything into tan nothing out. I tried expaning the brackets and collecting like terms, that didnt work out either.

2. Oct 4, 2005

### Astronuc

Staff Emeritus
3. Oct 4, 2005

### brandon26

Yeh, but I cant simplify anything to solve the problem

4. Oct 4, 2005

### Astronuc

Staff Emeritus
Well expand the sin and cos and apply cos (-x) = cos x, and sin (-x) = -sin x.

Then collect terms/coefficients of cos x and sin x.

If one has a form A cos x = B sin x, the tan x = A/B and x = tan-1 (A/B). In this problem A and B have terms of sin 10 and cos 10.
The text passage contains a mathematical question in the form of an equation to solve for x, and it also includes a discussion about the approaches taken to solve the problem and hints provided to solve it.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Homework Help: Component Identities

1. Oct 4, 2005

### brandon26

Solve for x

3sin(x+10)=4cos(x-10)

I tried changinf everything into tan nothing out. I tried expaning the brackets and collecting like terms, that didnt work out either.

2. Oct 4, 2005

### Astronuc

Staff Emeritus
3. Oct 4, 2005

### brandon26

Yeh, but I cant simplify anything to solve the problem

4. Oct 4, 2005

### Astronuc

Staff Emeritus
Well expand the sin and cos and apply cos (-x) = cos x, and sin (-x) = -sin x.

Then collect terms/coefficients of cos x and sin x.

If one has a form A cos x = B sin x, the tan x = A/B and x = tan-1 (A/B). In this problem A and B have terms of sin 10 and cos 10.
user
The text passage contains a mathematical question in the form of an equation to solve for x, and it also includes a discussion about the approaches taken to solve the problem and hints provided to solve it.

TYPE: SINGLE_QUESTION_WITH_ANSWER