How do you find the amplitude, period, and phase shift of $4 cos (3 θ + \frac{3}{2} π) + 2$ $4cos(3theta + 3/2pi) + 2$ ?

Question

How do you find the amplitude, period, and phase shift of $4 cos (3 θ + \frac{3}{2} π) + 2$ $4cos(3theta + 3/2pi) + 2$ ?

1 Answer

Impact of this question

2163 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-04T03:23:25

First, the range of the cosinus function is [-1;1]
$\to$ $rarr$ therefore the range of $4 cos (X)$ $4cos(X)$ is [-4;4]
$\to$ $rarr$ and the range of $4 cos (X) + 2$ $4cos(X)+2$ is [-2;6]

Second, the period $P$ $P$ of the cosinus function is defined as: $cos (X) = cos (X + P)$ $cos(X) = cos(X+P)$ $\to P = 2 π$ $rarr P = 2pi$ .
$\to$ $rarr$ therefore:

$(3 θ_{2} + \frac{3}{2} π) - (3 θ_{1} + \frac{3}{2} π) = 3 (θ_{2} - θ_{1}) = 2 π$ $(3theta_2+3/2pi)-(3theta_1+3/2pi) = 3(theta_2-theta_1) = 2pi$

$\to$ $rarr$ the period of $4 cos (3 θ + \frac{3}{2} π) + 2$ $4cos(3theta+3/2pi)+2$ is $\frac{2}{3} π$ $2/3pi$

Third, $cos (X) = 1$ $cos(X)=1$ if $X = 0$ $X=0$
$\to$ $rarr$ here $X = 3 (θ + \frac{π}{2})$ $X=3(theta+pi/2)$
$\to$ $rarr$ therefore $X = 0$ $X=0$ if $θ = - \frac{π}{2}$ $theta = -pi/2$
$\to$ $rarr$ therefore the phase shift is $- \frac{π}{2}$ $-pi/2$

Science

Math

Humanities

... and beyond

How do you find the amplitude, period, and phase shift of $4 cos (3 θ + \frac{3}{2} π) + 2$ $4cos(3theta + 3/2pi) + 2$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the amplitude, period, and phase shift of 4cos(3θ+32π)+24cos(3theta + 3/2pi) + 2?

1 Answer

Related questions

Impact of this question

How do you find the amplitude, period, and phase shift of $4 cos (3 θ + \frac{3}{2} π) + 2$ $4cos(3theta + 3/2pi) + 2$ ?