Precalculus B: Trigonometric Functions Unit Test

A fly is standing on a boulder, which is rolling down a hill. The forward torque the fly exerts on the boulder when it has rolled $$x$$  meters, in newton meters, is given by:

$$\qquad\tau(x)=\frac{2}{1000}\sin\left(\frac{2\pi(x+0.2)}{4}\right)$$

What is the midline of this function? Give an exact answer. You do not have to type in

$$y=$$

What is the value of $$\cos\left(\frac{\pi}{3}\right)$$ ?
Enter an exact value.

Find the following trigonometric values.
Express your answers exactly.

$$\cos\left(\frac{2\pi}{3}\right)=$$ ​ (a)  

$$\sin\left(\frac{2\pi}{3}\right)=$$ ​ (b)  

The graph of a sinusoidal function intersects its midline at   $$\left(0,\ 2\right)$$ and then has a minimum point at   $$\left(3,\ -6\right)$$ .

Write the formula of the function, where $$x$$   is entered in radians.

$$f\left(x\right)=$$

Be sure to write it in the form of:

$$A\sin\ or\ \cos\left(Bx\right)+D$$

Use 5 points (STARTING AT THE Y-INTERCEPT)

to plot the following sinusoidal function:

$$f\left(x\right)=2\cos\left(\frac{\pi}{4}x\right)+4$$

What is the phase shift in the following sinusoidal function?

$$h(x)=3\sin(2x-\pi)+2$$

Type in an exact answer.

What is the period in the following sinusoidal function?

$$h(x)=-3\sin(6x-\pi)+2$$

Type in an exact answer.

What is the amplitude in the following sinusoidal function?

$$h(x)=-3\sin(2x-\pi)+2$$

Type in an exact answer.