rewrite 2sin3x-4cos3x-5 into one function for graphing

[mdem1234]

Hi guys,

I have this function 2sin3x-4cos3x-5

I need to combine it into one function so I can graph it.

I have R=root (2^2+4^2) = root 20

cos theta= 2/root20, sin theta =4/root20

so theta=1.017

so my combined function is..

root20Sin(3x+1.107)-5

is this correct, I am a bit confused about theta and if it is in degrees or radians, and if it is in degrees, do i need to convert it into radians before i can graph it properly?.... if anyone could help me out that would be much appreciated, thanks

 

[royhaas]

Re: sin function

Your angle is in radians.

 

[soroban]

Re: sin function

Hello, mdem1234!

I have this function: $\displaystyle 2\sin3x-4\cos3x-5$

I need to combine it into one function so I can graph it.

I have: $\displaystyle R\:=\:\sqrt{2^2+4^2} \:=\:\sqrt{20}$

. . $\displaystyle \cos\theta\:=\:\frac{2}{\sqrt{20}},\quad\sin\theta \:=\:\frac{4}{\sqrt{20}}$

so: $\displaystyle \theta \:\approx\: 1.017$

So my combined function is: .$\displaystyle \sqrt{20}\sin(3x+1.107)-5$

is this correct? . . . . Yes!

I am a bit confused about theta and if it is in degrees or radians.

You already have $\displaystyle \theta$ in radians . . . good!

Nearly all advanced math is performed in radians.

. . "When in doubt, use radians."

 

[mdem1234]

Re: sin function

Thank you!!

 

[BigGlenntheHeavy]

Re: sin function

$\displaystyle f(x) = \sqrt(20)sin(3x+1.10715)-5, \ Wrong.$

$\displaystyle f(x) = \sqrt(20)sin(3x-1.10715)-5, \ Right.$

 

[mdem1234]

Re: sin function

$\displaystyle f(x) = \sqrt(20)sin(3x+1.10715)-5, \ Wrong.$

$\displaystyle f(x) = \sqrt(20)sin(3x-1.10715)-5, \ Right.$

Why is it minus and not plus 1.10715??

 

[Deleted member 4993]

because your original equation was

2sin3x - 4cos3x - 5