Chapter 1

Calculate each of the six trigonometric functions at angle \(\theta\) without using a calculator. \(\theta=\pi / 6\)

In Exercises 1-8, state the domain of the function defined by the given expression. $$ x /(1+x) $$

Plot the points \((2,-4),(7,3),(\sqrt{3}, \sqrt{6}),(\pi+3, \pi-3),\) \(\left(\pi^{2}, \sqrt{\pi}\right),(-8 / 3,-2 / \pi)\) on a set of coordinate axes.

In Exercises \(1-6,\) convert the decimal to a rational fraction. (Ellipses are included in some exercises to indicate repetition.) 2.13

Calculate each of the six trigonometric functions at angle \(\theta\) without using a calculator. \(\theta=\pi / 4\)

State the domain of the function defined by the given expression. $$ \sqrt{x^{2}+2} $$

Sketch, on the same set of axes, lines passing through point (1,3) and having slopes \(-3,-2,-1,0,1,2,\) and 3

Graph the set of points that satisfies \(y+x=3\)

Convert the decimal to a rational fraction. (Ellipses are included in some exercises to indicate repetition.) 0.00034

Calculate each of the six trigonometric functions at angle \(\theta\) without using a calculator. \(\theta=2 \pi / 3\)

Sketch, on the same set of axes, lines having slope -3 and passing through points \((-2,-7),(-1,0),(3,0),\) and (5,1).

Graph the set of points that satisfies \(y-x=2\).

Convert the decimal to a rational fraction. (Ellipses are included in some exercises to indicate repetition.)\(0.232323 \ldots\)

Calculate each of the six trigonometric functions at angle \(\theta\) without using a calculator. \(\theta=4 \pi / 3\)

State the domain of the function defined by the given expression. $$ \sqrt{2-x^{2}} $$

Sketch the line that passes through point (-2,5) and that rises 7 units for every 2 units of left-to-right motion.

Which of the points \((2,1),(3,0),(4,-1),\) or \((1 / 2,9 / 2)\) is farthest from the origin? Which is nearest to the origin? Which is farthest from (-5,6)\(?\) Which is nearest to (10,7)\(?\)

Convert the decimal to a rational fraction. (Ellipses are included in some exercises to indicate repetition.) \(2.222 \ldots\)

Calculate the given expression without using a calculator. \(\sin (\pi / 3) \sin (\pi / 6)\)

Write the point-slope equation of the line determined by the given data. Slope \(5,\) point (-3,7)

State the domain of the function defined by the given expression. $$ 1 /\left(x^{2}-1\right) $$

Let \(A=(2,3), B=(-4,7),\) and \(C=(-5,-6) .\) Calculate the distance of each of these points to each of the others.

Convert the decimal to a rational fraction. (Ellipses are included in some exercises to indicate repetition.) \(5.001001001 \ldots\)

Calculate the given expression without using a calculator. \(\cos (0)-\cos (\pi)\)

Write the point-slope equation of the line determined by the given data. Slope \(-2,\) point (4.1,8.2)

State the domain of the function defined by the given expression. $$ \sqrt{x} /\left(x^{2}+x-6\right) $$

The Cartesian equation of a circle is given. Sketch the circle and specify its center and radius. \((x+8)^{2}+(y-1)^{2}=16\)

Convert the decimal to a rational fraction. (Ellipses are included in some exercises to indicate repetition.) \(15.7231231231 \ldots\)

Calculate the given expression without using a calculator. \(\cos (\pi / 6)+\cos (\pi / 3)\)

Write the point-slope equation of the line determined by the given data. Slope \(-1,\) point \((-\sqrt{2}, 0)\)

State the domain of the function defined by the given expression. $$ \sqrt{x^{2}-4 x+5} $$

The Cartesian equation of a circle is given. Sketch the circle and specify its center and radius. \((x-1)^{2}+(y-3)^{2}=9\)

In Exercises \(7-12,\) use long division to convert the rational fraction to a (possibly nonterminating) decimal with a repeating block. Identify the repeating block. \(1 / 40\)

Calculate the given expression without using a calculator. \(\sin (\pi / 4) \cos (\pi / 4)\)

Write the point-slope equation of the line determined by the given data. Slope \(0,\) point \((-\pi, \pi)\)

State the domain of the function defined by the given expression. $$ 1 / \sqrt{\left(x^{2}-4\right)(x-1)} $$

The Cartesian equation of a circle is given. Sketch the circle and specify its center and radius. \(x^{2}+(y+7)^{2}=1\)

Use long division to convert the rational fraction to a (possibly nonterminating) decimal with a repeating block. Identify the repeating block. \(25 / 8\)

Calculate the given expression without using a calculator. \(\tan (\pi / 3) / \tan (\pi / 6)\)

Let \(F(x)=x^{2}+5, G(x)=(x+1) /(x-1),\) and \(H(x)=2 x-5 .\) Calculate the value of the given function at \(x\). \(G \circ(1 / G)\)

Write the point-slope equation of the line determined by the two given points. (2,7),(6,-4)

In Exercises 9-14, sketch the graph of the function defined by the given expression. $$ x^{2}+1 $$

The Cartesian equation of a circle is given. Sketch the circle and specify its center and radius. \(x^{2}+(y+5)^{2}=2\)

Use long division to convert the rational fraction to a (possibly nonterminating) decimal with a repeating block. Identify the repeating block.\(5 / 3\)

Calculate the given expression without using a calculator. \(\cos (2 \pi / 3) \csc (2 \pi / 3)\)

Write the point-slope equation of the line determined by the two given points. (12,1),(-4,-4)

Sketch the graph of the function defined by the given expression. $$ x^{2}-1 $$

The Cartesian equation of a circle is given. Sketch the circle and specify its center and radius. \((x-3)^{2}+y^{2}+y=1\)

Use long division to convert the rational fraction to a (possibly nonterminating) decimal with a repeating block. Identify the repeating block. \(2 / 7\)

In Exercises \(11-14\), write the function \(h\) as the composition \(h=g \circ f\) of two functions. (There is more than one correct way to do this.) \(h(x)=(x-2)^{2}\)