MHB Express 3sin(3x)-4cos(3x) in the form Rcos(3x+\alpha)

[ThomsonKevin]

Tried simplifying it of course, but didn't get far. Here's tbe problem:

''Express 3sin(3x)-4cos(3x) in the form Rcos(3x+\alpha),\alpha\ge0;R>0. Hence, find the smallest possible value of x for which 3sin(3x)-4cos(3x)=4.''

Bit confusing for me, especially the last part. How do you solve this, lads?

 

[topsquark]

Tried simplifying it of course, but didn't get far. Here's tbe problem:

''Express 3sin(3x)-4cos(3x) in the form Rcos(3x+\alpha),\alpha\ge0;R>0. Hence, find the smallest possible value of x for which 3sin(3x)-4cos(3x)=4.''

Bit confusing for me, especially the last part. How do you solve this, lads?

[math]a~cos(3x) + b~sin(3x) = \sqrt{a^2 + b^2}~cos \left ( 3x - tan^{-1} \left ( \frac{b}{a} \right ) \right )[/math]
where a = 3, b = -4. (Warning: We have to take x > 0 for this.)

You can find that identity (and many others) here.

-Dan