Mathematics, 20.01.2021 04:30 ariloveshorses

Write the equation of the trigonometric graph.

Answers: 3

Show answers

Answers

Answer from: rosieposie27

Answer(s):

$\displaystyle y = 2sin\:(x + \frac{\pi}{2}) - 2 \\ y = 2cos\:x - 2$

Explanation:

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

$\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 2$

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of $\displaystyle y = 2sin\:x - 2,$ in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted $\displaystyle \frac{\pi}{2}\:unit$ to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK $\displaystyle \frac{\pi}{2}\:unit,$ which means the C-term will be negative, and perfourming your calculations, you will arrive at $\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1}.$ So, the sine graph of the cosine graph, accourding to the horisontal shift, is $\displaystyle y = 2sin\:(x + \frac{\pi}{2}) - 2.$ Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits the origin $\displaystyle [0, 0],$ from there to $\displaystyle [2\pi, 0],$ they are obviously $\displaystyle 2\pi\:units$ apart, telling you that the period of the graph is $\displaystyle 2\pi.$ 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. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at $\displaystyle y = -2,$ in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Write the equation of the trigonometric graph.

Answer from: Quest

the answer to your question a or b but i am pretty sure it is b. i hope this : )

step-by-step explanation:

Answer from: Quest

google dat sis

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:30

Astick 2 m long is placed vertically at point b. the top of the stick is in line with the top of a tree as seen from point a, which is 3 m from the stick and 30 m from the tree. how tall is the tree?

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

Atown has a population of 12000 and grows at 3.5% every year. what will be the population after 7 years, to the nearest whole number?

Answers: 3

Answer

Mathematics, 22.06.2019 01:30

Sara goes on a slingshot ride in an amusement park. she is strapped into a spherical ball that has a radius 3*10^2 of centimeters. what is the volume of air in the spherical ball? use this formula: volume of a sphere=4/3pi,r^3 , where r is the sphere’s radius.

Answers: 1

Answer

Mathematics, 22.06.2019 02:20

Which of these could you find on a credit report? check all that apply. previous address current employer highest level of education completed bankruptcy and a civil court case monthly income late credit card payments

Answers: 2

Answer

You know the right answer?

Write the equation of the trigonometric graph.
...

Questions