Solve 3sin(x+10)=4cos(x-10) - Help!

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Homework Help Overview

The discussion revolves around solving the equation 3sin(x+10)=4cos(x-10), which involves trigonometric identities and manipulation of sine and cosine functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to manipulate the equation by converting terms into tangent and expanding brackets but reports difficulties in simplifying the expression. Some participants suggest using trigonometric identities for sine and cosine to aid in the simplification process.

Discussion Status

Participants are exploring various methods to simplify the equation, with some offering guidance on expanding trigonometric functions and collecting like terms. There is an ongoing examination of how to rearrange the equation into a form that can be solved for x, but no consensus has been reached on a specific approach.

Contextual Notes

There appears to be a challenge in simplifying the equation effectively, and participants are questioning the assumptions related to the transformations being applied. The original poster expresses frustration with the inability to simplify the problem, indicating potential constraints in their understanding of the identities involved.

brandon26
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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.
Please help.
 
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Yeh, but I can't simplify anything to solve the problem
 
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.
 

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