91Ó°ÊÓ

The table at the right shows the times for high tide and low tide. The markings on the side of a local pier showed a high tide of 7 \(\mathrm{ft}\) and a low tide of 4 \(\mathrm{ft}\) on the previous day. \(\begin{array}{cc}{\text { High tide }} & {4 : 03 \text { A.M. }} \\ {\text { Low tide }} & {10 : 14 \text { A.M. }} \\ {\text { High tide }} & {4 : 25 \text { P.M. }} \\ {\text { Low tide }} & {10 : 36 \text { P.M. }}\end{array}\) a. What is the average depth of water at the pier? What is the amplitude of the variation from the average depth? b. How long is one cycle of the tide? c. Write a cosine function that models the relationship between the depth of water and the time of day. Use \(y=0\) to represent the average depth of water. Use \(t=0\) to represent the time \(4 : 03\) A.M. d. Suppose your boat needs at least 5 \(\mathrm{ft}\) of water to approach or leave the pier. Between what times could you come and go?

Find a positive and a negative coterminal angle for the given angle. $$ 400^{\circ} $$

Find a positive and a negative coterminal angle for the given angle. $$ -425^{\circ} $$

Open-Ended. Draw an angle in standard position. Draw a circle with its center at the vertex of the angle. Find the measure of the angle in radians and degrees.

Find the next two terms in each sequence. Write a formula for the \(n\) th term. Identify each formula as explicit or recursive. $$ 3,6,11,18,27, \dots $$

In which quadrant, or on which axis, does the terminal side of each angle lie? $$ -60^{\circ} $$

For sound waves, the period and the frequency of a pitch are reciprocals of each other: period \(=\frac{\text { seconds }}{\text { cycle }}\) and frequency \(=\frac{\text { cycles }}{\text { second }} .\) Write an equation for each pitch. Let \(\theta=\) time in seconds, Use \(a=1\). the lowest pitch easily heard by humans: 30 cycles per second

Reasoning. Use the proportion \(\frac{\text { measure of central angle }}{\text { measure of one complete rotation }}=\frac{\text { length of arc }}{\text { circumference }}\) to derive the formula \(s=r \theta .\) Use \(\theta\) for the central angle measure and \(s\) for the arc length. Measure the rotation in radians.

Write the explicit formula for each geometric sequence. List the first five terms. $$ a_{1}=900, r=-\frac{1}{3} $$

a. Graph \(y-\tan x\) and \(y-\cot x\) on the same axes. b. State the domain, the range, and the asymptotes of each function. c. Writing Compare the two graphs. How are they alike? How are they different? d. Geometry The graph of the cotangent function can be reflected about a line to graph the tangent function. Name at least two lines that have this property.