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