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 is 288..

hope this

Answer from: Quest

Did you get there answer to 44?
Ineed 3 more questions done on this page numbers through 43-45

Another question on Mathematics

Mathematics, 21.06.2019 14:10

Given the function f(x) = log base 4(x+8) , find the value of f^-1(2)

Answers: 1

Answer

Mathematics, 21.06.2019 14:30

What is the prime factorization of 195

Answers: 2

Answer

Mathematics, 21.06.2019 15:50

Dylan and dusty plan to take weekly surfing lessons together. if the 2-hour lessons are $20 per person and they plan to spend $100 each on new surfboards, what is the maximum number of lessons the two can take if the total amount spent for lessons and surfboards is at most $480?

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

Explain step-by-step how to simplify -5(2x – 3y + 6z – 10).

Answers: 2

Answer

You know the right answer?

Write the equation of the trigonometric graph.
...

Questions