Use the table to write a proportion.
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13. The equation of the given function is
14. The equation of the cotangent function is
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( ), 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 =
∴ 4π =
- By using cross multiplication
∴ 4π(b) = 2π
- Divide both sides by 4π
∴ b =
∵ The phase shift is
∵ c is the phase shift
∴ c =
∵ 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
∴
You can write it as
The equation of the given function is
14.
y = cot[b(t + c)] + d
∵ The period = π
∵ The period is 2π/b
- Equate π by 2π/b to find b
∴ π =
- By using cross multiplication
∴ π(b) = 2π
- Divide both sides by π
∴ b = 2
∵ The phase shift is
∵ c is the phase shift
∴ c =
∵ 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
∴
The equation of the cotangent function is
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