Math
posted by jiya .
3 cos (ωt + 2) + 4 sin (ωt + 1) as A cos (ωt + φ) .
A = ? φ= ?

Math 
Steve
try the addition formulas:
3 cos (ωt + 2) = 3(cosωt cos2  sinωt sin2)
4 sin(ωt+1) = 4(sinωtcos1 + cosωtsin1)
adding them up you get
3cosωtcos2+4cosωtsin1
+ 4sinωtcos1  3sinωtcos2
Now, according to wolframalpha.com, that gives
A = √(2524sin(1))
tanφ =
sec(1)(4sin(1)+3cos(2))

4  6sin(1)
so φ ≈ 3.736
See
http://www.wolframalpha.com/input/?i=3+cos+%28t+%2B+2%29+%2B+4+sin+%28t+%2B+1%29
But I don't see any clear path to getting there.
Respond to this Question
Similar Questions

physics
The angle of the pendulum is given by θ = θmcos(ωt + φ), where ω = 3.24 rad/s. If at t = 0, θ = 1 rad and dθ/dt = 0.9 rad/s, what are φ and θm? 
Physics
At t=0, a wave disturbance has the waveform that is shown in a figure. The wave has a velocity of 500.0 m/s to the left. What's the values for k and ω if the wave equation is to be written in the form: y(x,t)=A cos(kx±ωt+φo). … 
Physics
Two sinusoidal waves with the same amplitude of 9.11 mm and the same wavelength travel together along a string that is stretched along an x axis. Their resultant wave is shown twice in the figure, as valley A travels in the negative … 
Physics
Two sinusoidal waves with the same amplitude of 9.11 mm and the same wavelength travel together along a string that is stretched along an x axis. Their resultant wave is shown twice in the figure, as valley A travels in the negative … 
Physics
A circuit contains a selfinductance L in series with a capacitor C and a resistor R. This circuit is driven by an alternating voltage V=V0sin(ωt). We have L=0.015 H, R= 80 Ω, C= 5e06 F, and V0=40 volts. (a) What is the … 
Physics
Ey=E0sin(kx−ωt), Ez=4E0sin(kx−ωt), the magnetic field can be written in the following way B =[ sin(ωt+(−1)bBkx)(cBxˆ+dByˆ+eBzˆ)] In other words: Bx=cBsin(ωt+(−1)bBkx), By=dBsin(ωt+(−1)bBkx), … 
trig help much appreciated! :))
1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove that … 
Calculus question
It looks very complicated and I do not know how to even start. Any help would be immensely appreciated. A pendulum has a mass, m, suspended from a rod of length L. At the time t = 0, the pendulum is pulled through an angle θ0 … 
Math
write 3 cos (ωt + 2) + 4 sin (ωt + 1) as A cos (ωt + φ). Find A = ? 
Physics
A box of mass m slides down an inclined plane that makes an angle of φ with the horizontal. If the coefficient of kinetic friction is μk, find an expression for the acceleration of the box down the slope. The acceleration …