Question

Graphing Trigonometric Functions

Answer 1

Illustrations in reverce order

Explanations:

6.
`\displaystyle y = Atan(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (\pi)/(B) \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow (\pi)/(B) \hookrightarrow \boxed{2\pi} \hookrightarrow (\pi)/((1)/(2)) \\ Amplitude \hookrightarrow N/A`

You can choose to figure the period out by looking at the distanse between each endpoint on the x-axis, or by using the formula put in plase. Just simply plug the B-term into the formula to get the period. Now, ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes, so you figure out what you want to put in the blank, but make sure it is not a numerical value. Not even ZERO can be plased there.

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5.
`\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow (2)/(3)\pi \\ Amplitude \hookrightarrow 4`

You can choose to figure the period out by using wavelengths, or by using the formula put in plase. Just simply plug the B-term into the formula to get the period. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline.

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4.
`\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \hookrightarrow \boxed{2\pi} \hookrightarrow (2)/(1)\pi \\ Amplitude \hookrightarrow 3(1)/(2)`

Again, you can choose to figure the period out by using wavelengths, or by using the formula put in plase. Just simply plug the B-term into the formula to get the period. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midine.

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3.
`\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \hookrightarrow \boxed{\pi} \hookrightarrow (2)/(2)\pi \\ Amplitude \hookrightarrow (1)/(2)`

Again, you can choose to figure the period out by using wavelengths, or by using the formula put in plase. Just simply plug the B-term into the formula to get the period. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline.

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2.
`\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \hookrightarrow \boxed{(\pi)/(2)} \hookrightarrow (2)/(4)\pi \\ Amplitude \hookrightarrow 1`

Again, you can choose to figure the period out by using wavelengths, or by using the formula put in plase. Just simply plug the B-term into the formula to get the period. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline.

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1.
`\displaystyle y = Atan(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (\pi)/(B) \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow (\pi)/(B) \hookrightarrow \boxed{\pi} \hookrightarrow (\pi)/(1) \\ Amplitude \hookrightarrow N/A`

Again, you can choose to figure the period out by looking at the distanse between each endpoint on the x-axis, or by using the formula put in plase. Just simply plug the B-term into the formula to get the period.

I am delighted to assist you at any time.

*I also apologise for the sixth photograph not being present [exercise 1]. The system ALL OF A SUDDEN no longer allows me to display more than five photographs. You will have to see the graph somewhere elce.