Equations of sin & cos Functions

A water wave is created in a wave tank. It has an amplitude of 3 and a period of

 $\frac{4\pi}{5}$ .  Find the equation of this wave as a sine function. 

•  $f\left(t\right)=3\sin\ \frac{5t}{2}$  

•  $f\left(t\right)=\frac{5}{2}\sin3t$  

•  $f\left(t\right)=\frac{4\pi}{5}\sin\ \frac{t}{3}$  

•  $f\left(t\right)=3\sin\ \frac{4\pi t}{5}$  

What is the amplitude and period of $f\left(t\right)=-2\cos\left(3t\right)?$  

• amplitude: 4  period:  $\frac{2\pi}{3}$  

• amplitude: 2  period:  $\frac{3\pi}{2}$  

• amplitude: -2  period:  $\frac{3\pi}{2}$  

• amplitude: 2  period:  $\frac{2\pi}{3}$  

Tags

CCSS.HSF-IF.C.7E

Find a function for the graph.

• $f\left(t\right)=3\sin6t$

• $f\left(t\right)=6\cos3t$

• $f\left(t\right)=-3\sin3t$

• $f\left(t\right)=3\sin3t$

Tags

CCSS.HSF-IF.C.7E

 $f\left(t\right)=-5\sin\left(7t-1\right)$  

What are the amplitude, period, and phase shift of the given function?

• amplitude: 10  period:  $\frac{2\pi}{7}$    phase shift:  $\frac{1}{7}$  

• amplitude: 5  period:  $\frac{2\pi}{7}$    phase shift:  $\frac{1}{7}$  

• amplitude: -5  period:  $2\pi$    phase shift:  $-\frac{1}{7}$  

• amplitude: 5  period:  $4\pi$    phase shift:  $-\frac{1}{7}$  

Tags

CCSS.HSF-IF.C.7E

 $f\left(t\right)=-\frac{2}{3}\cos\left(3t-3\pi\right)$  

What are the amplitude, period, and phase shift of the given function?

• amplitude:  $\frac{2}{3}$    phase shift:  $\pi$   period:  $\frac{2\pi}{3}$  

• amplitude: 1   phase shift:  $3\pi$   period:  $\frac{2\pi}{3}$  

• amplitude:  $-\frac{2}{3}$    phase shift:  $\pi$   period:  $3\pi$  

• amplitude:  $\frac{2}{3}$      phase shift:  $\pi$   period:  $3\pi$ 

Tags

CCSS.HSF-IF.C.7E

What is the equation of the function?

• $f\left(x\right)=7\sin\left(3\left(x-\frac{\pi}{2}\right)\right)+3$

• $f\left(x\right)=7\sin\left(3\left(x-2\right)\right)-3$

• $f\left(x\right)=7\sin\left(3\left(x+\frac{\pi}{2}\right)\right)+3$

• $f\left(x\right)=-7\sin\left(3\left(x-\frac{\pi}{2}\right)\right)-3$

Tags

CCSS.HSF-IF.C.7E

Which graph represents $f\left(x\right)=-4\cos x$  

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Tags

CCSS.HSF-IF.C.7E

 $f\left(x\right)=9\sin x+1$  

Which graph represents

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Tags

CCSS.HSF-IF.C.7E

Choose all the transformations that change the graph of $f\left(t\right)=\sin t$  into the graph of  $g\left(t\right)=-9\sin t-2$  

• Translation down 2

• Reflection over the y axis

• Reflection of the x axis

• Translation up 2

• Rotation of 9 degrees

Tags

CCSS.HSF-IF.C.7E

Write a sine function with the amplitude of 3; period of $\pi$ and vertical shift of 5. 

Tags

CCSS.HSF-IF.C.7E