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ClassLink 6:53 PM Tue Apr 30
AA
ixl.com
big lip characters - Google Search
Volume of cubes and rectangular...
Volume of cubes and rectangular...
Find an equation for a sinusoidal function that has period
pi, amplitude 1 , and contains the point
(-(3pi)/(4),4).
Write your answer in the form
f(x)=Asin(Bx+C)+D, where
A,B,C, and
D are real numbers.

f(x)=
Submit

ClassLink $6$ : $53$ PM Tue Apr $30$ $\newline$ AA $\newline$ ixl.com $\newline$ big lip characters - Google Search $\newline$ Volume of cubes and rectangular... $\newline$ Volume of cubes and rectangular... $\newline$ Find an equation for a sinusoidal function that has period $\pi$ , amplitude $1$ , and contains the point $\left(-\frac{3 \pi}{4}, 4\right)$ . $\newline$ Write your answer in the form $\mathrm{f}(\mathrm{x})=\mathrm{A} \sin (\mathrm{Bx}+\mathrm{C})+\mathrm{D}$ , where $\mathrm{A}, \mathrm{B}, \mathrm{C}$ , and $\mathrm{D}$ are real numbers. $\newline$ $f(x)=$ $\newline$ Submit

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Write equations of cosine functions using properties

Full solution

Q. ClassLink

6

:

53

PM Tue Apr

30

\newline

AA

\newline

ixl.com

\newline

big lip characters - Google Search

\newline

Volume of cubes and rectangular...

\newline

Volume of cubes and rectangular...

\newline

Find an equation for a sinusoidal function that has period

\pi

, amplitude

1

, and contains the point

\left(-\frac{3 \pi}{4}, 4\right)

.

\newline

Write your answer in the form

\mathrm{f}(\mathrm{x})=\mathrm{A} \sin (\mathrm{Bx}+\mathrm{C})+\mathrm{D}

, where

\mathrm{A}, \mathrm{B}, \mathrm{C}

, and

\mathrm{D}

are real numbers.

\newline

f(x)=

\newline

Submit

Calculate Period: The period of a sinusoidal function is given by $2\pi/B$ . Given the period is $\pi$ , we set $B = 2\pi/\pi = 2$ .
Find C and D: We have: $A = 1$ and $B = 2$ . To find C and D, we use the point $(-\frac{3\pi}{4}, 4)$ . The general form is $f(x) = A\sin(Bx + C) + D$ . Plugging in the values, we get: $4 = 1\sin(2(-\frac{3\pi}{4}) + C) + D$ $4 = \sin(-\frac{3\pi}{2} + C) + D$
Solve for C: Since $\sin(-\frac{3\pi}{2}) = -1$ , the equation becomes: $\newline$ $4 = -1 + D + \sin(C)$ $\newline$ To solve for C, we need $\sin(C) = 0$ (since $-1 + D + 0 = 4$ must hold for D to be a real number). Possible values for C where $\sin(C) = 0$ are $C = n\pi$ , where $n$ is an integer.
Solve for $D$ : Choosing $C = 0$ (simplest case), we then solve for $D$ : $4 = -1 + D$ $D = 5$
Substitute Values: Substituting $A = 1$ , $B = 2$ , $C = 0$ , and $D = 5$ into the equation $f(x) = A\sin(Bx + C) + D$ gives us: $\newline$ $f(x) = \sin(2x) + 5$

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