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
nataly862011 [7]
3 years ago
9

Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

Mathematics
1 answer:
garik1379 [7]3 years ago
8 0

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is z'(x) = \frac{1}{2}  + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right).

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be z (x) = \cos x the base formula, where x is measured in sexagesimal degrees. This expression must be transformed by using the following data:

T = 180^{\circ} (Period)

z_{min} = -4 (Minimum)

z_{max} = 5 (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of 2\pi radians. In addition, the following considerations must be taken into account for transformations:

1) x must be replaced by \frac{2\pi\cdot x}{180^{\circ}}. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

\Delta z = \frac{z_{max}-z_{min}}{2}

\Delta z = \frac{5+4}{2}

\Delta z = \frac{9}{2}

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

z_{m} = \frac{z_{min}+z_{max}}{2}

z_{m} = \frac{1}{2}

The new function is:

z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)

Given that z_{m} = \frac{1}{2}, \Delta z = \frac{9}{2} and T = 180^{\circ}, the outcome is:

z'(x) = \frac{1}{2}  + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

You might be interested in
zoey made 6 3/4 cups of fruit salad for a picnic they ate 1/3 of the fruit salad for a picnic they ate 1/3 of the fruit salad Ho
liberstina [14]
They ate 2 3/4 cups?
3 0
3 years ago
Amy ran 3/4 a mile. Write the distance Amy ran as a decimal.
dem82 [27]
0.75 of a mile Amy ran
6 0
3 years ago
Read 2 more answers
2x+3 less than or equal to 5
rjkz [21]
2x+3 \leq 5 \\  \\ (2x+3)-3 \leq (5)-3 \\  \\ 2x \leq 2 \\  \\   \frac{2x}{2}  \leq  \frac{2}{2}  \\  \\ x \leq 1 \\  \\x=( -\infty} ,1]
6 0
3 years ago
Read 2 more answers
HELP PLEASE
Alexxandr [17]
About 89 gallons of gas
5 0
2 years ago
Read 2 more answers
How can you determine if a number is a rational number
Murljashka [212]
Rational numbers can be written as a fraction
7 0
3 years ago
Other questions:
  • Find two points for this equation<br> 2x+3y=12
    5·1 answer
  • How many chords can be there in a circle
    14·2 answers
  • If one of two parallel lines is perpendicular to another line, the other of the two lines is ________ to the third line.
    6·2 answers
  • What's smaller 4/5 or 7/10
    8·2 answers
  • What is the F.O.I.L method in Algerbra 1?
    15·2 answers
  • How many thousands are in 20 hundreds?
    6·1 answer
  • (64/25)^-3/2 x (64)^1/3​
    12·1 answer
  • A beekeeper pours honey into jars. Each large jar holds 18 ounces of honey. Each small jar holds 12 ounces of honey. The beekeep
    10·1 answer
  • A circle has a radius 30 cm. What is the area? Show your<br> work.
    6·1 answer
  • Write 7,062.01 in expanded form
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!