Chapter 14

Find each value. $$ \sin \left(\cos ^{-1} \frac{2}{3}\right) $$

Find the first five terms of the sequence in which \(a_{1}=3, a_{n+1}=2 a_{n}+5\)

The graph of the equation \(y=2 \cos \theta\) is shown. Which is a solution for \(2 \cos \theta=1 ?\) F. \(\frac{8 \pi}{3}\) G. \(\frac{13 \pi}{3}\) H. \(\frac{10 \pi}{3}\) J. \(\frac{15 \pi}{3}\)

Simplify each expression. $$ \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{2}}{2} $$

Simplify each expression. \(\csc \theta \tan \theta+\sec \theta\)

Write an equation of a parabola with focus at \((11,-1)\) and directrix \(y=2 .\) (lesson \(10-2 )\)

Find each value. $$ \cos \left(\cos ^{-1} \frac{4}{7}\right) $$

PREREQUISITE SKILL Graph each pair of functions on the same set of axes. $$ y=x^{2}, y=3 x^{2} $$

Find the exact value of \(\sin 2 \theta, \cos 2 \theta, \sin \frac{\theta}{2},\) and \(\cos \frac{\theta}{2}\) for each of the following. \(\sin \theta=\frac{3}{5} ; 0^{\circ}<\theta<90^{\circ}\)

Write each expression in quadratic form, if possible. $$ a^{8}-7 a^{4}+13 $$

Simplify each expression. $$ \frac{1}{2} \cdot \frac{\sqrt{2}}{2} $$

A pilot is flying from Chicago to Columbus, a distance of 300 miles. In order to avoid an area of thunderstorms, she alters her initial course by \(15^{\circ}\) and flies on this course for 75 miles. How far is she from Columbus?

TEACHING Ms. Granger has taught 288 students at this point in her career. If she has 30 students each year from now on, the function \(S(t)=288+30 t\) gives the number of students \(S(t)\) she will have taught after \(t\) more years. How many students will she have taught after 7 more years?

Find each value. $$ \sin ^{-1}\left(\sin \frac{5}{6}\right) $$

PREREQUISITE SKILL Graph each pair of functions on the same set of axes. $$ y=3 x^{2}, y=3 x^{2}-4 $$

Find the exact value of \(\sin 2 \theta, \cos 2 \theta, \sin \frac{\theta}{2},\) and \(\cos \frac{\theta}{2}\) for each of the following. \(\cos \theta=\frac{1}{2} ; 0^{\circ}<\theta<90^{\circ}\)

Simplify each expression. $$ \frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{2} $$

PREREQUISITE SKILL Name the property illustrated by each statement. If \(4+8=12,\) then \(12=4+8\)

Find each value. $$ \cos \left(\tan ^{-1} \frac{3}{4}\right) $$

PREREQUISITE SKILL Graph each pair of functions on the same set of axes. $$ y=2 x^{2}, y=2(x+1)^{2} $$

Find the exact value of \(\sin 2 \theta, \cos 2 \theta, \sin \frac{\theta}{2},\) and \(\cos \frac{\theta}{2}\) for each of the following. \(\cos \theta=\frac{5}{6} ; 0^{\circ}<\theta<90^{\circ}\)

Simplify each expression. $$ \frac{1}{2}-\frac{\sqrt{3}}{4} $$

Solve each equation. \(x^{2}=\frac{20}{16}\)

GEOMETRY Find the total number of diagonals that can be drawn in a decagon.

Find the exact value of \(\sin 2 \theta, \cos 2 \theta, \sin \frac{\theta}{2},\) and \(\cos \frac{\theta}{2}\) for each of the following. \(\sin \theta=\frac{4}{5} ; 0^{\circ}<\theta<90^{\circ}\)

Find each value if \(f(x)=x^{2}-7 x+5\) \(f(2)\)

Solve each equation. \(x^{2}=\frac{9}{25}\)

Solve each equation. Round to the nearest hundredth. $$ 4^{x}=24 $$

Find the exact value of each expression. \(\sin 240^{\circ}\)

Find each value if \(f(x)=x^{2}-7 x+5\) \(f(0)\)

Solve each equation. \(x^{2}=\frac{5}{25}\)

PREREQUISITE SKILL Name the property illustrated by each statement. If \(q+(8+5)=32,\) then \(q+13=32\)

Solve each equation. Round to the nearest hundredth. $$ 4.3^{3 x+1}=78.5 $$

Find the exact value of each expression. \(\cos 315^{\circ}\)

Find each value if \(f(x)=x^{2}-7 x+5\) \(f(-3)\)

Solve each equation. \(x^{2}=\frac{18}{32}\)

Solve each equation. Round to the nearest hundredth. $$ 7^{x-2}=53^{-x} $$

Find the exact value of each expression. \(\sin 150^{\circ}\)

Simplify each expression. $$ \frac{3}{a-2}+\frac{2}{a-3} $$

PREREQUISITE SKILL Solve each equation. $$ (x+6)(x-5)=0 $$

Simplify each expression. $$ \frac{w+12}{4 w-16}-\frac{w+4}{2 w-8} $$

PREREQUISITE SKILL Solve each equation. $$ (x-1)(x+1)=0 $$

Simplify each expression. $$ \frac{3 y+1}{2 y-10}+\frac{1}{y^{2}-2 y-15} $$

PREREQUISITE SKILL Solve each equation. $$ x(x+2)=0 $$

Find the value of each function. $$ \cos 150^{\circ} $$

PREREQUISITE SKILL Solve each equation. $$ (2 x-5)(x+2)=0 $$

Find the value of each function. $$ \tan 135^{\circ} $$

PREREQUISITE SKILL Solve each equation. $$ (2 x+1)(2 x-1)=0 $$

Find the value of each function. $$ \sin \frac{3 \pi}{2} $$

PREREQUISITE SKILL Solve each equation. $$ x^{2}(2 x+1)=0 $$