The table gives the amount of daylight, in hours and minutes, in Sydney, Australia, on the first day of every month. Determine the period of time during a year when Sydney gets a minimum of 12 hours of daylight.

Day	Jan. 1	Feb. 1	Mar. 1	Apr. 1	May 1	June 1	July 1	Aug. 1	Sept. 1	Oct. 1	Nov. 1	Dec. 1
Amount of daylight (h:min)	14:22	13:44	12:49	11:44	10:45	10:03	9:56	10:27	11:23	12:25	13:27	14:13

Data as ordered pairs with days of year and decimal hours: (1,14.37),(32,13.73),(60,12.82),(91,11.73)$, (121, 10.75), (152, 10.05), (182, 9.93), (213, 10.45), (244, 11.38), (274, 12.42),$(305,13.45),(335,14.22)

The table gives the monthly mean maximum temperature, in degrees Celsius, for Canberra, Australia. Roughly fit a sine model of the form y=a $\sin \frac{1}{b}$(x-h)+k to the data. Then determine a sine regression model using a graphing calculator. Finally, visually differentiate between the two models in relation to the data.

Explain how the domain, range, maximum values, and minimum values compare between the sine and cosine functions and their reciprocals.

Determine the new function after the given transformation.

$$h(x)=0.8(x-8)^2-10$$

7 units left, 4 units up

While completing an assignment in class, students were required to recognize the period and amplitude of a trigonometric function without graphing the function. Roland said that the function f(x)=4 $\sin \left(\frac{1}{2} x\right)$ has a period of 4 and an amplitude of $\frac{1}{2}$.Determine and correct his mistaske.

Plot $g(x)=-3 \tan \frac{x}{2}$.

In a science class lab, a mass is suspended from a spring above a tabletop. The mass is pulled down and released. By examining frames from a video as the mass bobs up and down, the class obtains the model h(t)=5 $\sin 4(t-0.39)+10$ for the height h of the mass above the tabletop at time $t$ in seconds. Cassandra notices that after several seconds the mass is not bobbing up and down as far, but it still seems to take about the same time for a cycle. Plot $y=e^{-0.05 x}[5 \sin 4(x-0.39)]+10$ on a graphing calculator with the original model for $0 \leq x \leq 10$. State how this model differs from the original model, and how it might account for Cassandra's observation.

For the trigonometric function, determine the vertical stretch or compression and the horizontal stretch or compression. Then, plot the function and ifnd its period.

$$y=-\frac{1}{4} \cos 3 x$$

Do transformed functions of the form $f(x)=a \tan \left(\frac{1}{b} x\right)$ have the same behavior seen in the parent function, that is, f(-x)=-f(x) ? Justify your answer and how it helps to graph transformed functions.

For the trigonometric function, determine the vertical stretch or compression and the horizontal stretch or compression. Then, plot the function and ifnd its period.

$$y=\frac{1}{3} \sin 2 x$$

Graph one cycle of the transformed tangent function g(x) together with the parent function f(x)=tan x. g(x)=-$\frac{1}{4} \tan 4 x$

Why does it make sense that a graphing calculator has a sine regression option but not a cosine regression option?

Determine the new function after the given transformation.

$$q(x)=-0.5(x+2)^2-12$$

6 units down

Hannah is graphing the functions f(x)=5 $\sin (x)$ and g(x)=5 $\csc (x)$ on the same coordinate plane. State what she should see if she graphs them correctly.