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Algebra 2 Help

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Jan 19, 2018

#1
+17163
+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

Jan 19, 2018

#1
+17163
+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
#2
+99117
+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

https://www.desmos.com/calculator/bluugr6nna

Jan 22, 2018