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3 years ago

Explain how the graph of y = 2csc(x - pi/4) - 5 is related to the graph of the basic trigonometric function y = cscx.

1 answer:

3 0

Answer: The distance between the min and max increased by a factor of 2, horizontally shifted to the right by $\bold{\dfrac{\pi}{4}}$ , shifted down 5 units, and has a phase shift of $\bold{\dfrac{\pi}{4}}$

Step-by-step explanation:

The general form of a csc function is: y = A csc (Bx - C) + D where

|A| is the amplitude (vertical stretch)
-A is a reflection over the x-axis
|B| is the horizontal stretch
-B is a reflection over the y-axis
C is a horizontal shift (left or right)
D is a vertical shift (up or down)

Period is $\dfrac{2\pi}{B}$
Phase Shift is $\dfrac{C}{B}$

In the given transformed graph y = 2 csc (x - $\dfrac{\pi}{4}$ ) - 5

A = 2 --> distance between the Min and max is 2(2) = 4
C = $\dfrac{\pi}{4}$ --> horizontally shifted to the right $\dfrac{\pi}{4}$ units
D = -5 --> shifted DOWN 5 units
Phase shift is $\dfrac{\pi}{4}$

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(1+2i) (2+5i)

Lostsunrise [7]

Answer:

Step-by-step explanation:

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2+5i+4i+10i^2

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3 years ago

Which of the following illustrates a phase shift?

Natasha_Volkova [10]

Answer:

A. y = -2 - cos(x-π)

Explanation:

The general form of the trig equation is:

y = A sin (Bx + C) + D

where:

A is the amplitude

$\frac{2\pi}{B}$ is the period

$\frac{-C}{B}$ is the phase shift

D is the vertical shift

Now, let's check the choices:

A. y = -2 - cos(x-π)

$\frac{-C}{B} = \frac{\pi}{1} = \pi$

Therefore, the function has a phase shift of π

B. y = 3 cos(4x)

$\frac{-C}{B} = \frac{0}{4} = 0$

Therefore, the function has no phase shift

C. y = tan(2x)

$\frac{-C}{B} = \frac{0}{2} = 0$

Therefore, the function has no phase shift

D. y = 1 + sin(x)

$\frac{-C}{B} = \frac{0}{1} = 0$

Therefore, the function has no phase shift

Based on the above, the correct answer is A

Hope this helps :)

3 0

3 years ago

Read 2 more answers

Ann car can go 117 miles on 3 gallons of gas. During a drive last weekend, Ann used 8 gallons of gas. How far did she drive?

Nitella [24]

Answer:

Ann drove 312 miles in 8 gallons.

Step-by-step explanation:

Distance covered by Ann's car = 117 miles

Gallons of gas spent by Ann's car to cover 117 miles = 3 gallons

Unit rate = 117 miles / 3 gallons

= 39 miles per gallon

so Ann's car can go 39 miles in one gallon of gas.

Given that Ann used 8 gallons of gas.

Therefore,

Distance covered by Ann's car in 8 gallons = 39 × 8

= 312 miles

Therefore, Ann drove 312 miles in 8 gallons.

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3 years ago

Example of how is the quadratic equation used in nursing?

Mumz [18]

Answer:

Nurses use this to calculate dosage needed for patients, calculating drip rates and conversion between systems.

Step-by-step explanation:

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3 years ago

HELP ASAP PLEASE AND EXPLAIN:)

olganol [36]

Answer:

5=a

the answer is a

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2 years ago