precalc question!

Question

precalc question!

anonymous · Answer

attachment

anonymous · Answer

I'll help. Give me one moment. Nice user pic by the way

anonymous · Answer

okay thanks..and double thanks lol..

amistre64 · Answer

$$y=Atrig(\omega (x+\rho ))$$

anonymous · Answer

Amplitude of the cos function is one (as is the sin).  Since there is no coefficient multiplying the function, the amplitude is one.  The three is a vertical translation, and does has no effect on the amplitude.

The period of cos x is 2pi.  The coefficient of three on the x makes is go faster, so the period is divided by three; the period of cos(3x) is 2pi/3.

The phase shift is a little tricky.  We need to factor out the factor of three from the argument of the cos function, so it is cos (3(x-pi/3)).  From this it's easy to identify the phase shift as pi/3.

anonymous · Answer

it helps if you factor out the 3 so x is by itself. So when you rewrite the equation, it's cos 3(x-pi/3)+3. Then, the period for cos is 2pi/B. B is 3, so the period is 2pi/3. the phase shift is pi/3. the amplitude is 1 - the number before cos.  the three is the vertical translation