1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitrij [34]
3 years ago
14

Answer questions 13. And 14. Please! Show minimal work...

Mathematics
1 answer:
ale4655 [162]3 years ago
5 0

13. The equation of the given function is y=4sin[\frac{(t-\frac{4}{3})}{2}]-2

14. The equation of the cotangent function is y=cot[2(t-\frac{1}{3})]+2

Step-by-step explanation:

Let us revise the transformation of the trigonometric function:

y = a f[b(x + c)] + d, where

  • Amplitude is a
  • f represents the trigonometry function
  • Period is 2π/b
  • Phase shift is c (positive is to the left)
  • Vertical shift is d

13.

∵ y = a sin( \frac{2\pi t}{T} ), where a is the amplitude

   and T is the wave in seconds

∵ The amplitude is 4

∴ a = 4

∵ The period is 4π

∴ T = 4π

From the rules above

∵ The period is 2π/b

∴ T = \frac{2\pi }{B}

∴ 4π = \frac{2\pi }{b}

- By using cross multiplication

∴ 4π(b) = 2π

- Divide both sides by 4π

∴ b = \frac{1}{2}

∵ The phase shift is -\frac{4}{3}\pi

∵ c is the phase shift

∴ c = -\frac{4}{3}\pi

∵ The vertical shift is -2

∵ d is the vertical shift

∴ d = -2

Now substitutes the values of a, b, c and d in the form of the equation below

∵ y = a sin[b(t + c)] + d

∴ y=4sin[\frac{1}{2}(t-\frac{4}{3})]-2

You can write it as y=4sin[\frac{(t-\frac{4}{3})}{2}]-2

The equation of the given function is y=4sin[\frac{(t-\frac{4}{3})}{2}]-2

14.

y = cot[b(t + c)] + d

∵ The period = π

∵ The period is 2π/b

- Equate π by 2π/b to find b

∴ π = \frac{2\pi }{b}

- By using cross multiplication

∴ π(b) = 2π

- Divide both sides by π

∴ b = 2

∵ The phase shift is -\frac{1}{3}\pi

∵ c is the phase shift

∴ c = -\frac{1}{3}\pi

∵ The vertical shift is 2

∵ d is the vertical shift

∴ d = 2

Now substitutes the values of b, c and d in the form of the equation below

∵ y = cot[b(t + c)] + d

∴ y=cot[2(t-\frac{1}{3})]+2

The equation of the cotangent function is y=cot[2(t-\frac{1}{3})]+2

Learn more:

You can learn more about trigonometry function in brainly.com/question/3568205

#LearnwithBrainly

You might be interested in
3.2 cm on the map correspond to 4 km in the actual distance?
geniusboy [140]

Answer:

Step-by-step explanation:

Here, 3.2 centimeters on the map is equivalent to 4 kilometers. We can use unitary method to find, how many kilometer/kilometers each centimeter corresponds to. Using the unitary method: Therefore, the scale of map represents 1.25 kilometers for each centimeter.

6 0
4 years ago
Lindsay has scored 15 goals in 10 lacrosse games this season. a) What is her unit rate of scoring? b) How many goals might Linds
pashok25 [27]
A)1.5 goals per match
b) 1.5x35= 52.5 so 53
Assuming she is consistent
8 0
3 years ago
5(4+6) please help :((((
erastovalidia [21]
The answis 50 :)))))(
8 0
3 years ago
Read 2 more answers
Name three numbers between 3.65 and 3.66
Dmitry_Shevchenko [17]
Three numbers between 3.65 and 3.66 could be:

1) 3.651
2) 3.655
3) 3.657
4) 3.659

Hope this helps! :)
7 0
3 years ago
Find the missing angle measures<br> m∠3<br> m∠4<br> m∠5<br> m∠6<br> Please show work
Alla [95]

Answer:

75

Step-by-step explanation:

x+45+60=180

x+105=180

x=180-105

x=75

7 0
3 years ago
Other questions:
  • In triangle PQR, angle P is congruent to angle R and the measure of angle Q is twice the measure of angle R. Find the measure of
    7·2 answers
  • Triangle PIG was rotated to create triangle P'I'G'. Describe the transformation using details and degrees.
    11·1 answer
  • So for the remaining angles
    12·2 answers
  • HSDhDfhDhDcgjdjdjzffnzfggnDdt
    15·1 answer
  • Which number is the smallest? A) 1.28 x 10-4 B) 2.85 x 10-6 C) 3.24 x 10-5 D) 5.48 x 10-8
    7·2 answers
  • A large pizza has diameter 36 cm and a medium pizza has diameter 30 cm. What is the difference in area of the pizzas? Round your
    7·1 answer
  • F(n) = 2f(n-1) +2
    5·2 answers
  • Write equation in point slope form of the line that passes through the given point with the given slope (-3/2, 6); m=-1
    7·1 answer
  • Solve. x+y+z=6 3x−2y+2z=2−2x−y+3z=−4
    5·1 answer
  • Find the values of x for which the denominator is equal to zero for y=3x+5/x-6.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!