#1**+2 **

First One: Looks like a cosine wave inverted (multiplied by -1) and the AMPLITUDE is reduced by 1/2

soooo: -1/2 cos x

2: Frequency is 1/period period is pi frequency then would be 1/pi

3: Looks like a sine wave but the period is pi .....so the frequency is DOUBLED

sooooo: sin 2x

4: Similar to #3 the frequency is doubled (2x) so the period is HALVED to pi

ElectricPavlov
Jan 19, 2018

#1**+2 **

Best Answer

First One: Looks like a cosine wave inverted (multiplied by -1) and the AMPLITUDE is reduced by 1/2

soooo: -1/2 cos x

2: Frequency is 1/period period is pi frequency then would be 1/pi

3: Looks like a sine wave but the period is pi .....so the frequency is DOUBLED

sooooo: sin 2x

4: Similar to #3 the frequency is doubled (2x) so the period is HALVED to pi

ElectricPavlov
Jan 19, 2018

#2**+1 **

\(y=a* cos[n(\theta+p) ]+ L\)

Amplitude =a

phase shift = p (units in the NEGATIVE direction - opposite direction to what most people expect)

wave length \(\lambda = \frac{2\pi}{n}\)

L is the vertical shift

SO CONSIDER

\(y=1.8cos(3\theta+\frac{\pi}{2})-1.5\\ rewrite\;\; as \\ y=1.8cos(3[\theta+\frac{\pi}{6}])-1.5\\\)

It has the basic \(y=cos(\theta) \)shape.

wavelength = \(\frac{2\pi}{3}\)

Phase (horizontal) shift =\( \frac{\pi}{6}\;\)units in the __negative__ direction

Amplitude =1.8

Vertical shift is 1.5 units DOWN

check

Here is the graph.

You can play iwth the circles on the left to see how I 'developed' the graph

Melody
Jan 22, 2018