Chapter 13

Find one angle with positive measure and one angle with negative measure coterminal with each angle. \(\frac{17 \pi}{4}\)

Find each probability if a coin is tossed 4 times \(P(\text { exactly } 2 \text { heads })\)

Use synthetic substitution to find \(f(3)\) and \(f(-4)\) for each function. $$ f(x)=-3 x^{2}+2 x-1 $$

ACT/SAT If the cotangent of angle \(\theta\) is \(1,\) then the tangent of angle \(\theta\) is $$ \begin{array}{lll}{\mathbf{A}-1} & {} & {\mathbf{C}} & {1} \\ {\mathbf{B}} & {0} & {} & {\mathbf{D}} & {3}\end{array} $$

Some sport-utility vehicles (SUVs) use 15-inch radius wheels. When driven 40 miles per hour, determine the measure of the angle through which a point on the wheel travels every second. Round to both the nearest degree and the nearest radian.

Find each probability if a coin is tossed 4 times \(P(4 \text { heads })\)

Use synthetic substitution to find \(f(3)\) and \(f(-4)\) for each function. $$ f(x)=4 x^{2}-10 x+5 $$

REVIEW Which angle has a tangent and cosine that are both negative? $$ \begin{array}{lll}{\mathbf{F}} & {110^{\circ}} & {\mathbf{H}} & {210^{\circ}} \\\ {\mathbf{G}} & {180^{\circ}} & {\mathbf{J}} & {340^{\circ}}\end{array} $$

Suppose the gondolas on the Navy Pier Ferris Wheel were numbered from 1 through 40 consecutively in a counterclockwise fashion. If you were sitting in gondola number 3 and the wheel were to rotate counterclockwise through \(\frac{47 \pi}{10}\) radians, which gondola used to be in the position that you are in now?

Find each probability if a coin is tossed 4 times \(P(\text { at least } 1 \text { head })\)

Rewrite each degree measure in radians and each radian measure in degrees. (lesson \(13-2 )\) \(90^{\circ}\)

Solve each equation \(y^{4}-64=0\)

Rewrite each degree measure in radians and each radian measure in degrees. (lesson \(13-2 )\) \(\frac{5 \pi}{3}\)

Draw and label an example of an angle with negative measure in standard position. Then find an angle with positive measure that is coterminal with this angle.

Solve each equation \(x^{5}-5 x^{3}+4 x=0\)

Solve each equation \(d+\sqrt{d}-132=0\)

UTFRAIURE In one of Grimm's Fairy Tales, Rumpelsititskin has the ability to spin straw into gold. Suppose on the first day, he spun 5 pieces of straw into gold, and each day thereafter he spun twice as much. How many pieces of straw would he have spun into gold by the end of the week? (lesson \(11-4\) )

If \((a, b)\) is on a circle that has radius \(r\) and center at the origin, prove that each of the following points is also on this circle. a. \((a,-b)\) b. \((b, a)\) c. \((b,-a)\)

Find each product. Include the appropriate units with your answer. 5 gallons \(\left(\frac{4 \text { quarts }}{1 \text { gallon }}\right)\)

Use Cramer's Rule to solve each system of equations. $$ \begin{array}{l}{3 x-4 y=13} \\ {-2 x+5 y=-4}\end{array} $$

Express \(\frac{1}{8}\) of a revolution in degrees.

Find each product. Include the appropriate units with your answer. 6.8 miles \(\left(\frac{5280 \text { feet }}{1 \text { mile }}\right)\)

Use Cramer's Rule to solve each system of equations. $$ \begin{array}{l}{5 x+7 y=1} \\ {3 x+5 y=3}\end{array} $$

Find each product. Include the appropriate units with your answer. \(\left(\frac{2 \text { square meters }}{5 \text { dollars }}\right) 30\) dollars

Use Cramer's Rule to solve each system of equations. $$ \begin{array}{l}{2 x+3 y=-2} \\ {-6 x+y=-34}\end{array} $$

Choose the radian measure that is equal to \(56^{\circ} .\) A. \(\frac{\pi}{15}\) B. \(\frac{7 \pi}{45}\) C. \(\frac{14 \pi}{45}\) D. \(\frac{\pi}{3}\)

Find each product. Include the appropriate units with your answer. \(\left(\frac{4 \text { liters }}{5 \text { minutes }}\right) 60\) minutes

PREREQUISITE SKILL Solve each equation. Round to the nearest tenth. $$ \frac{a}{\sin 32^{\circ}}=\frac{8}{\sin 65^{\circ}} $$

Angular velocity is defined by the equation \(\omega=\frac{\theta}{t},\) where \(\theta\) is usually expressed in radians and \(t\) represents time. Find the angular velocity in radians per second of a point on a bicycle tire if it completes 2 revolutions in 3 seconds. F. \(\frac{\pi}{3}\) G. \(\frac{\pi}{2}\) H. \(\frac{2 \pi}{3}\) J. \(\frac{4 \pi}{3}\)

PREREQUISITE SKILL Solve each equation. Round to the nearest tenth. $$ \frac{b}{\sin 45^{\circ}}=\frac{21}{\sin 100^{\circ}} $$

PREREQUISITE SKILL Solve each equation. Round to the nearest tenth. $$ \frac{c}{\sin 60^{\circ}}=\frac{3}{\sin 75^{\circ}} $$

Find the margin of sampling error. \(p=72 \%, n=100\)

Find the margin of sampling error. \(p=50 \%, n=200\)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. choosing an arrangement of 5 CDs from your 30 favorite CDs

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. choosing 3 different types of snack foods out of 7 at the store to take on a trip

Find \([g \circ h](x)\) and \([h \circ g](x)\) \(g(x)=2 x\) \(h(x)=3 x-4\)

Find \([g \circ h](x)\) and \([h \circ g](x)\) \(g(x)=2 x+5\) \(h(x)=2 x^{2}-3 x+9\)

Simplify each expression. \(\frac{2}{\sqrt{3}}\)

Simplify each expression. \(\frac{3}{\sqrt{5}}\)

Simplify each expression. \(\frac{4}{\sqrt{6}}\)

Simplify each expression. \(\frac{5}{\sqrt{10}}\)

Simplify each expression. \(\frac{\sqrt{7}}{\sqrt{2}}\)

Simplify each expression. \(\frac{\sqrt{5}}{\sqrt{8}}\)