Question

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

Answer 1

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

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