How Do You Convert a Trigonometric Expression to a General Sine Function?

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Homework Help Overview

The problem involves expressing the function f(x) = -2sin(3x) - 4cos(3x) in the form of a general sine function, while also identifying its amplitude, period, and phase shift.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between sine and cosine functions, particularly in terms of expressing one as a phase-shifted version of the other. There are attempts to set up equations based on the general form of a sine function and to solve for parameters like amplitude and phase shift.

Discussion Status

The discussion is ongoing, with participants exploring different mathematical relationships and equations relevant to the problem. Some guidance has been offered regarding the setup of simultaneous equations, but no consensus or resolution has been reached yet.

Contextual Notes

Participants express uncertainty about how to begin the problem and question the implications of the equations they are forming. There is a mention of specific values for x that may influence the equations being considered.

KingKai
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Homework Statement



Express the function f(x) = -2sin(3x) -4cos(3x) in the form of a general sine finction.

Identify the amplitude, period, and phase shift

Homework Equations



sinx/cosx = tanx

sin2x + cos2x = 1


The Attempt at a Solution




don't know how to start
don't penalize me for this.
 
Physics news on Phys.org
If you wanted to express cos(x) as sin(x+a), then a is the phase shift.
What would a have to be?
 
A sin(B x + C) + D=A sin(C) cos(B x)+A cos(C) sin(B x)+D
so solve simultaneously the equations

A cos(C) sin(B x)=-2sin(3x)
A sin(C) cos(B x)=-4cos(3x)
D=0
 
lurflurf said:
A sin(B x + C) + D=A sin(C) cos(B x)+A cos(C) sin(B x)+D
so solve simultaneously the equations

A cos(C) sin(B x)=-2sin(3x)
A sin(C) cos(B x)=-4cos(3x)
D=0

The equations are valid for every value of x. The zeroes of sin(Bx) are at x=k∏/3, k integer. What should be B?

What are the equations at x=0, x=π/6?

ehild
 

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