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What is the amplitude, period, phase shift and vertical displacement of y=3sin(3x+pi)-1? | HIX Tutor

<blockquote>
<mathjax>#"the standard form of the sine function is"#</mathjax>
<mathjax>#color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))#</mathjax>
<mathjax>#"where amplitude "=|a|," period "=(2pi)/b#</mathjax>
<mathjax>#"phase shift "=-c/b" and vertical shift "=d#</mathjax>
<mathjax>#"here "a=3,b=3,c=pi" and "d=-1#</mathjax>
<mathjax>#"amplitude "=|3|=3" period "=(2pi)/3#</mathjax>
<mathjax>#"phase shift "=-pi/3" vertical shift "=-1#</mathjax>
</blockquote>

<blockquote>
<mathjax>#"the standard form of the sine function is"#
<mathjax>#color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))#
<mathjax>#"where amplitude "=|a|," period "=(2pi)/b#
<mathjax>#"phase shift "=-c/b" and vertical shift "=d#
<mathjax>#"here "a=3,b=3,c=pi" and "d=-1#
<mathjax>#"amplitude "=|3|=3" period "=(2pi)/3#
<mathjax>#"phase shift "=-pi/3" vertical shift "=-1#
</blockquote>

Emery Adkins

Let's break it down step by step!

1. Amplitude: The amplitude of a sine function tells us how high it goes. In this case, the amplitude is 3.

2. Period: The period tells us how long it takes for one complete cycle of the sine function. To find the period, we can use the formula T = 2π/b, where b is the coefficient of x in the equation. In this case, b = 3, so the period is T = 2π/3.

3. Phase Shift: The phase shift tells us how much the sine function is shifted horizontally. To find the phase shift, we need to isolate the inside of the sine function. In this case, the inside is 3x + π. To find the phase shift, set 3x + π equal to zero and solve for x. For this equation, x = -π/3.

4. Vertical Displacement: The vertical displacement tells us how the graph has shifted vertically up or down. In this case, the vertical displacement is -1, which means the graph has shifted down by 1 unit.

In summary:
- Amplitude: 3
- Period: 2π/3
- Phase Shift: -π/3
- Vertical Displacement: -1

I hope this helps! Let me know if you have any more questions.

What is the amplitude, period, phase shift and vertical displacement of #y=3sin(3x+pi)-1#?