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3 years ago

What is the amplitude, period, and phase shift of f(x) = -4 sin(2x + π) - 5?

Mathematics

2 answers:

creativ13 [48]3 years ago

7 0

Answer:

Amplitude of the function is 4, period of the function is π and phase shift of the function is $-\frac{\pi}{2}$ .

Step-by-step explanation:

The given function is

$f(x)=-4\sin(2x+\pi)-5$ .... (1)

The general form of a sine function is

$f(x)=A\sin(Bx+C)+D$ .... (2)

where, |A| is amplitude, $\frac{2\pi}{B}$ is period, $-\frac{C}{B}$ is phase shift and D is midline.

From (1) and (2) we get

$A=-4,B=2, C=\pi,D=-5$

$|A|=|-4|=4$

Amplitude of the function is 4.

$\frac{2\pi}{B}=\frac{2\pi}{2}=\pi$

Period of the function is π.

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

Therefore the phase shift of the function is $-\frac{\pi}{2}$ .

son4ous [18]3 years ago

3 0

F(x) = -4sin(2x + π) - 5

<u>Amplitude</u>
A = -π

<u>Period</u>
<u>2π</u> = <u>2π</u> = π
B 2

<u>Phase Shift</u>
<u>-C</u> = <u>-π</u> = ≈ 1.57<u>
</u> B 2<u>
</u>

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18. Angle B is approximately 26.0 degrees.

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Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

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$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

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Start by finding the cosine of angle B. Apply the law of cosine.

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