Graphing Trig. Functions

Write an equation of the given trig function:

• sin

• Amp = 3

• Period = 4π

• Phase Shift = π

• Vertical Shift = -2

Write an equation of the given trig function:

• sec

• Amp = 1

• Period = 90

• Phase Shift = 45

• Vertical Shift = 1

Amplitude = 6

Period= 360

Phase Shift = -45

Vertical Shift = 2

Amplitude = None

Period = 4

Phase Shift = None

Vertical Shift = -3

A carousel makes 2.625 revolutions per minute. Convert revolutions per minute to radians per second.

0.275 radians / second

The tires on a car have a diameter of 30 inches. If the tires are running at a rate of 2000 revolutions per minute, determine the car’s speed in miles per hour. Hint: Remember 1 mile = 5280 feet.

178.5 mph

A bicycle wheel is 27 inches in diameter. Suppose the wheel turns at a constant rate of 2.75 revolutions per second. What is the linear speed in miles per hour of a point on the tire.

13.25 mph

Find the value of θ: sin θ = -1

θ = 270° / 270° + 360°k

Cos θ = 0

θ = 90°

Sec θ is undefined

θ = 90°

A leaf flots on the water bobbing up and down. The distance between its highest and lowest point is 4 cm. It moves from its highest point down to its lowest point and back to its highest point every 12 seconds. Write a function that models the movement of the lear in the relationship to the equilibrium point.

y = 2 sin 30x

Write a sine function which models the oscillation of tides in Savannah, GA, if the equilibrium point is 4.24 feet, amplitude is 3.55 feet, phase shift -4.68 hours and period is 12.8 hours.

y = 3.55 sin π/6.4 (x + 4.68) + 4.24

Write the transformed trig function:

y = 2 cos 2 (x - π) - 3

Write the equation for the inverse of the function AND graph both the original function and its inverse:

y = arcsin(x)

Inverse: f ⁻¹(x) = sin x

Write the equation for the inverse of the function AND graph both the original function and its inverse:

y = Cos (x) - 3

Inverse: f ⁻¹(x) = Cos ⁻¹ (x + 3)

Graph y = Tan (x)

Evaluate the following:

½

Evaluate the following:

0