Write an equation of the cosine function with each amplitude and period. amplitude = 1.5, period = $5 \pi$

Determine each angular displacement in radians. Round to the nearest tenth. 2.7 revolutions

Write the equation for the inverse of each function. Then graph the function and its inverse. $y=\arccos x$

State the phase shift for each function. Then graph each function. $y=\sin (\theta-2 \pi)$

The average monthly temperatures for the city of Honolulu, Hawaii, are given below.

$$\begin{matrix} \text{Jan} & \text{Feb} & \text{Mar} & \text{Apr} & \text{May} & \text{Jun} & \text{Jul} & \text{Aug} & \text{Sep} & \text{Oct} & \text{Nov} & \text{Dec}\\ \ {73^{\circ}} & \ {73^{\circ}} & \ {74^{\circ}} & \ {76^{\circ}} & \ {78^{\circ}} & \ {79^{\circ}} & \ {81{\circ}} & \ {81^{\circ}} & \ {81^{\circ}} & \ {80^{\circ}} & \ {77^{\circ}} & \ {74^{\circ}}\\ \end{matrix}$$

According to your model, what is the average temperature in May? How does this compare to the actual average?

The average monthly temperatures for the city of Honolulu, Hawaii, are given below.

$$\begin{matrix} \text{Jan} & \text{Feb} & \text{Mar} & \text{Apr} & \text{May} & \text{Jun} & \text{Jul} & \text{Aug} & \text{Sep} & \text{Oct} & \text{Nov} & \text{Dec}\\ \ {73^{\circ}} & \ {73^{\circ}} & \ {74^{\circ}} & \ {76^{\circ}} & \ {78^{\circ}} & \ {79^{\circ}} & \ {81{\circ}} & \ {81^{\circ}} & \ {81^{\circ}} & \ {80^{\circ}} & \ {77^{\circ}} & \ {74^{\circ}}\\ \end{matrix}$$

According to your model, what is the average temperature in August? How does this compare to the actual average?

The average monthly temperatures for the city of Honolulu, Hawaii, are given below.

$$\begin{matrix} \text{Jan} & \text{Feb} & \text{Mar} & \text{Apr} & \text{May} & \text{Jun} & \text{Jul} & \text{Aug} & \text{Sep} & \text{Oct} & \text{Nov} & \text{Dec}\\ \ {73^{\circ}} & \ {73^{\circ}} & \ {74^{\circ}} & \ {76^{\circ}} & \ {78^{\circ}} & \ {79^{\circ}} & \ {81{\circ}} & \ {81^{\circ}} & \ {81^{\circ}} & \ {80^{\circ}} & \ {77^{\circ}} & \ {74^{\circ}}\\ \end{matrix}$$

Write a sinusoidal function that models the monthly temperatures, using t = 1 to represent January.

Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to $\frac{\pi}{2}$ to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle. What is the circumference of the equator?

If a person has a blood pressure of 130 over 70, then the person's blood pressure oscillates between the maximum of 130 and a minimum of 70. Graph the equation.

Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to $\frac{\pi}{2}$ to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle. Which latitude circle has a circumference of about 3593 kilometers?

The average monthly temperatures for the city of Honolulu, Hawaii, are given below.

$$\begin{matrix} \text{Jan} & \text{Feb} & \text{Mar} & \text{Apr} & \text{May} & \text{Jun} & \text{Jul} & \text{Aug} & \text{Sep} & \text{Oct} & \text{Nov} & \text{Dec}\\ \ {73^{\circ}} & \ {73^{\circ}} & \ {74^{\circ}} & \ {76^{\circ}} & \ {78^{\circ}} & \ {79^{\circ}} & \ {81{\circ}} & \ {81^{\circ}} & \ {81^{\circ}} & \ {80^{\circ}} & \ {77^{\circ}} & \ {74^{\circ}}\\ \end{matrix}$$

What is the period of a sinusoidal function that models the monthly temperatures?

The average monthly temperatures for the city of Honolulu, Hawaii, are given below.

$$\begin{matrix} \text{Jan} & \text{Feb} & \text{Mar} & \text{Apr} & \text{May} & \text{Jun} & \text{Jul} & \text{Aug} & \text{Sep} & \text{Oct} & \text{Nov} & \text{Dec}\\ \ {73^{\circ}} & \ {73^{\circ}} & \ {74^{\circ}} & \ {76^{\circ}} & \ {78^{\circ}} & \ {79^{\circ}} & \ {81{\circ}} & \ {81^{\circ}} & \ {81^{\circ}} & \ {80^{\circ}} & \ {77^{\circ}} & \ {74^{\circ}}\\ \end{matrix}$$

Find the vertical shift of a sinusoidal function that models the monthly temperatures.

Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to $\frac{\pi}{2}$ to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle. Write an equation for the circumference of any latitude circle with angle $\theta$.

Find each value by referring to the graph of the sine or the cosine function. $\cos 8 \pi$