Representing Sinusoidal Functions

What is the equation for this sinusoidal function?

• $f\left(x\right)=3\cos\left[60\left(x-1\degree\right)\right]-2$

• $f\left(x\right)=-3\cos\left[60\left(x-1\degree\right)\right]-2$

• $f\left(x\right)=3\sin\left[60\left(x-1\degree\right)\right]-2$

• $f\left(x\right)=-3\sin\left[60\left(x-1\degree\right)\right]-2$

Which is NOT an equation for this sinusoidal function?

• $f\left(x\right)=3\cos\left[60\left(x-1\degree\right)\right]-2$

•  $f\left(x\right)=-3\cos\left[60\left(x-4\degree\right)\right]-2$ 

•  $f\left(x\right)=3\sin\left[60\left(x-4\degree\right)\right]-2$ 

•  $f\left(x\right)=-3\sin\left[60\left(x-2.5\degree\right)\right]-2$ 

What is the equation for this sinusoidal function?

• $f\left(x\right)=2\cos\left(90x\right)-3$

• $f\left(x\right)=2\sin\left(90x\right)-3$

• $f\left(x\right)=2\cos\left(4x\right)-3$

• $f\left(x\right)=2\sin\left(4x\right)-3$

What is the equation for this sinusoidal function that uses cos?

•  $f\left(x\right)=2\cos\left[4\left(x+1\degree\right)\right]-3$ 

•  $f\left(x\right)=2\cos\left[90\left(x-1\degree\right)\right]-3$ 

•  $f\left(x\right)=-2\cos\left[4\left(x+1\degree\right)\right]-3$ 

•  $f\left(x\right)=-2\cos\left[90\left(x-1\degree\right)\right]-3$ 

Which is NOT an equation for this sinusoidal function?

•  $f\left(x\right)=-2\sin\left[90\left(x+2\degree\right)\right]-3$ 

• $f\left(x\right)=2\sin\left(90x\right)-3$

•  $f\left(x\right)=-2\sin\left[90\left(x-2\degree\right)\right]-3$ 

•  $f\left(x\right)=-2\sin\left[90\left(x-3\degree\right)\right]-3$ 

What is the equation of a sinusoidal function with amplitude 7, period 10, equilibrium of -3 and starts at a minimum value?

• $f\left(x\right)=7\cos\left(10x\right)-3$

• $f\left(x\right)=-7\cos\left(36x\right)-3$

• $f\left(x\right)=7\cos\left(36x\right)-3$

• $f\left(x\right)=-7\cos\left(10x\right)-3$

What is the equation of a sinusoidal function with amplitude 0.5, period 720, equilibrium of 2 and starts at a maximum value?

•  $f\left(x\right)=0.5\cos\left(0.5x\right)+2$ 

•  $f\left(x\right)=2\sin\left(0.5x\right)+0.5$ 

•  $f\left(x\right)=0.5\cos\left(2x\right)+0.5$ 

•  $f\left(x\right)=0.5\sin\left(0.5x\right)+0.5$ 

What is the equation of a sinusoidal function with a maximum point at  $\left(20,\ 30\right)$  and the next minimum point at  $\left(50,\ 40\right)$ ?

•  $f\left(x\right)=10\cos\left[12\left(x-20\degree\right)\right]+30$ 

•  $f\left(x\right)=5\sin\left[6\left(x-20\degree\right)\right]+30$ 

•  $f\left(x\right)=5\cos\left[6\left(x-20\degree\right)\right]+35$ 

•  $f\left(x\right)=10\sin\left[12\left(x-20\degree\right)\right]+35$ 

What is the equation of a sinusoidal function that starts at its equilibrium of -4 and then goes up to a maximum at  $\left(5,-1\right)$ ?

•  $f\left(x\right)=-4\sin\left(20x\right)-1$ 

•  $f\left(x\right)=3\sin\left(18x\right)-4$ 

•  $f\left(x\right)=-4\sin\left(18x\right)-1$ 

•  $f\left(x\right)=3\sin\left(20x\right)-4$ 

You get on a Ferris wheel car at its lowest point, 5 m above the ground level.  After 5 minutes, you are at the highest point, 65 m above ground level.  Determine an equation for  $h\left(t\right)$ , the height above the ground after t minutes

•  $h\left(t\right)=-30\cos\left(10t\right)+35$ 

•  $h\left(t\right)=-35\cos\left(36t\right)+30$ 

•  $h\left(t\right)=-35\cos\left(10t\right)+30$ 

•  $h\left(t\right)=-30\cos\left(36t\right)+35$