Help pls ! This is trigonometric function

Answer:

Amplitude: 4

Period: π

midline: y = 1

Step-by-step explanation:

r(x) = -4 sin(2x) + 1

r(x) = a sin(bx + c) + d where |a| is the amplitude and |b| for the period

a = -4         |a| = 4 :   Amplitude = 4

b = 2          |b| = 2     period of sin(x) = 2π

                                period of sin(bx + c) = 2π/|b| = 2π/2 = π

range of sin(2x) ... -1 ≤ sin(2x) ≤ 1

range of -4 sin(2x) + 1: -4+1 ≤ -4 sin(2x) + 1 ≤ 4+1    

-3 ≤ -4 sin(2x) + 1 ≤ 5

midline: y = (-3 + 5) / 2 = 1        y = 1

Answer:

Part A: The amplitude [tex]\displaystyle r[/tex]is [tex]\displaystyle 4.[/tex]

Part B: The period of [tex]\displaystyle r[/tex]is [tex]\displaystyle \pi.[/tex]

Part C: The equation of the midline of [tex]\displaystyle r[/tex]is [tex]\displaystyle y = 1.[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{r(x) = -4cos\:(2x - \frac{\pi}{2}) + 1} \\ \\ r(x) = 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 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle r(x) = 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 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

Keep in mind that although this IS a sine function, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the centre photograph displays the trigonometric graph of [tex]\displaystyle r(x) = -4cos\:2x + 1,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine 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 cosine graph [centre photograph] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle r(x) = -4cos\:(2x - \frac{\pi}{2}) + 1.[/tex]So, with all that being said, to find the period, again, take a look at the above information next to [tex]\displaystyle Wavelength\:[Period].[/tex]Now, the amplitude is obvious to figure out because it is the A-term. Moreover, the midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 1,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Anil scored 30 runs in the first innings of a test match. His score changed by +30 runs in the second innings. What was his score in the second innings?

please helpp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Which of the following are the sines for the angles of this triangle? Select all that apply.

Sandy pays $120 for 4 violin lessons. How much does she pay for 8 violin lessons?

Andy buys shoes that are on sale for 25% off the regular price. If the sale price is $36.45, what was the regular price of the shoes to the nearest cent?​

2) Find the median.
4,9, 1, 4, 6, 2, 3,1
A) 1 and 4
B) 3.5
C) 3.75
D) 8
pls help me show work

9. The ratio of boys to girls in Mrs. Reeves's class is 4 to 5. There are 20 girls in the
class.
What is the total number of students in Mrs. Reeves's class?

Find the perimeter of the rectangle in yards.

Elizabeth invests $7567 in a savings account with a fixed annual interest rate of 5% compounded quarterly. What will the account balance be after 7 years?

Major arc CBD measures 300 degrees. Which is the radian measure of its corresponding central angle? O 4 pie/3 O 5 pie/6 O 5 pie/3 O 11 pie/6

HELP ASAP
Write the equation of the line that passes through the points (1,-4) and (4, -5).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line

what’s the answers because this is stressing me?? plz help

Convert 121

5

to mixed fraction.​

Colin predicted whether he got answers right or wrong in his 50 question exam.
He identified the 12 questions he thought he got wrong.
It turns out that Colin got 5 questions right that he thought he got wrong.
Colin also got a total score of 42 out of 50 in the test.
What is the percentage accuracy he had with predicting his scores

Find the following angles from the above rectangle. ( answer only 5-12) please :)

5.
Find the rate of change for the situation. You run 3 miles in one hour and 6 miles in two hours.


A. 3 miles

B. 3 miles per hour

C. 2 hours

D. 2 miles per hour

The volume of a 3 cm cube is
O 9 cu cm
O 12 cu cm
O 6 cu cm
O 27 cu cm

Can someone please help me with math.

A small theater had 6 rows of 26 chairs each. An extra 9 chairs have just been brought in. How many chairs are in the theater now?

Please I need help with this problem

Joanne deposited $10,000 into an account that earns 5.5% compound interest, compounded annually. How much interest will Joanne earn after 10 years

if the probaility that it will rain tomorrow is 1/5 what is the probaility that it will not rain tomorrow

Help me plz will give Brainly est

The rectangle below has an area of 15k4 +35k3+20k2

What is the width and length

pls help me asap for brainlest

Need help with this;

Ms. Benson is making a jewelry box using 2 identical squares of wood and 4 identical rectangular pieces of wood, as shown below.



What is the surface area of the jewelry box in square inches (sq. in)?

ava gathered data about the age of runners and the time it took them to complete a 5K race and half marathon. Her data is displayed in the given scatter plots

A television and DVD player cost a total of $990. The cost of the television is two times the cost of the DVD player. Find the cost of each item.

At a birthday party, Vivian counts 15 vanilla ice cream cups and 25 chocolate ice cream cups. Which properties can be used to determine the percent, p, of the ice cream that is chocolate?