Find each value by referring to the graphs of the trigonometric functions. $\tan (-8 \pi)$

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 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?

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?

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.

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. If the person's pulse rate is 60 beats a minute, write a sine equation that models his or her blood pressure using t as time in seconds.

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 $\theta$.

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. The radius of Earth is about 6400 kilometers. Find the circumference of a great circle.

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 amplitude of a sinusoidal function that models the monthly temperatures.

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. Write the equation for the midline about which this person's blood pressure oscillates.

Determine each angular displacement in radians. Round to the nearest tenth. 3 revolutions