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

[KingKai]

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.

 

[SteamKing]

If you wanted to express cos(x) as sin(x+a), then a is the phase shift.
What would a have to be?

 

[lurflurf]

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

 

[ehild]

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