Chapter 5

Use the definition of \(f(x)\) as given by the following table. $$\begin{array}{|r|r|} \hline x & f(x) \\ \hline -2 & 5 \\ \hline -1 & 3 \\ \hline 1 & -2 \\ \hline 4 & -1 \\ \hline \end{array}$$ Find \(f^{-1}(-2)\)

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$f(x)=\tan x-3$$

Fill in the blank with one of the following: upward, downward, to the left, to the right. The graph of \(f(x)+3\) is obtained by shifting the graph of \(f(x)\) ____________ by 3 units.

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. In Exercises \(1-4,\) determine cehether the given points lie on the unit circle. That is, determine whether they satisfy the equation. $$(0,-1)$$

Find the circumference of each circle given its radius or diameter. Leave your answer in terms of \(\pi .\) radius 2 inches

Find the missing dimension of a right triangle with sides a and \(b\) and hypotenuse c. $$a=3, b=4, c=$$

Use the definition of \(f(x)\) as given by the following table. $$\begin{array}{|r|r|} \hline x & f(x) \\ \hline -2 & 5 \\ \hline -1 & 3 \\ \hline 1 & -2 \\ \hline 4 & -1 \\ \hline \end{array}$$ Find \(f^{-1}(-1)\)

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$f(x)=\tan x+2$$

Fill in the blank with one of the following: upward, downward, to the left, to the right. The graph of \(f(x)-2\) is obtained by shifting the graph of \(f(x)\) ____________ by 2 units.

Find the circumference of each circle given its radius or diameter. Leave your answer in terms of \(\pi .\) radius 5 inches

Find the missing dimension of a right triangle with sides a and \(b\) and hypotenuse c. $$a=6, b=8, c=$$

Use the definition of \(f(x)\) as given by the following table. $$\begin{array}{|r|r|} \hline x & f(x) \\ \hline -2 & 5 \\ \hline -1 & 3 \\ \hline 1 & -2 \\ \hline 4 & -1 \\ \hline \end{array}$$ Find \(\left(f \circ f^{-1}\right)(4)\)

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$f(x)=\sec x+1$$

Fill in the blank with one of the following: upward, downward, to the left, to the right. The graph of \(f(x+1)\) is obtained by shifting the graph of \(f(x)\) ____________ by 1 unit.

Find the circumference of each circle given its radius or diameter. Leave your answer in terms of \(\pi .\) diameter 12 inches

Find the missing dimension of a right triangle with sides a and \(b\) and hypotenuse c. $$a=2, b=3, c=$$

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$f(x)=\csc x-2$$

Use the definition of \(f(x)\) as given by the following table. $$\begin{array}{|r|r|} \hline x & f(x) \\ \hline -2 & 5 \\ \hline -1 & 3 \\ \hline 1 & -2 \\ \hline 4 & -1 \\ \hline \end{array}$$ Find \(\left(f^{-1} \circ f\right)(4)\)

Fill in the blank with one of the following: upward, downward, to the left, to the right. The graph of \(f(x-4)\) is obtained by shifting the graph of \(f(x)\) __________ by 4 units.

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. In Exercises \(1-4,\) determine cehether the given points lie on the unit circle. That is, determine whether they satisfy the equation. $$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$

Find the circumference of each circle given its radius or diameter. Leave your answer in terms of \(\pi .\) diameter 8 inches

Find the missing dimension of a right triangle with sides a and \(b\) and hypotenuse c. $$a=1, b=4, c=$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\arcsin 1$$

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$g(x)=\cot x+\frac{3}{2}$$

Fill in the blank with one of the following: horizontal, vertical. The graph of \(2 f(x)\) is obtained by a _________ stretch of the graph of \(f(x)\) by a factor of 2

Identify the quadrant in which each point lies. $$(-2,-1)$$

Determine the quadrant where the terminal side of the given angle lies. $$\frac{4 \pi}{3}$$

Find the missing dimension of a right triangle with sides a and \(b\) and hypotenuse c. $$a=3, c=6, b=$$

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$g(x)=\csc x-\frac{1}{2}$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\arccos 1$$

Fill in the blank with one of the following: horizontal, vertical. The graph of \(f(3 x)\) is obtained by a _________ compression of the graph of \(f(x)\) by a factor of \(\frac{1}{3}\)

Identify the quadrant in which each point lies. $$(1,5)$$

Determine the quadrant where the terminal side of the given angle lies. $$-\frac{5 \pi}{4}$$

Find the missing dimension of a right triangle with sides a and \(b\) and hypotenuse c. $$b=4, c=10, a=$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$f(x)=\tan \left(x+\frac{\pi}{4}\right)$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\arccos (-1)$$

Fill in the blank with one of the following: horizontal, vertical. The graph of \(f\left(\frac{1}{2} x\right)\) is obtained by a _________ stretch of the graph of \(f(x)\) by a factor of 2

In Exercises \(5-8,\) identify the quadrant in which each point lies. $$(3,-4)$$

Determine the quadrant where the terminal side of the given angle lies. $$310^{\circ}$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$f(x)=\tan \left(x-\frac{\pi}{2}\right)$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\arcsin 0$$

Fill in the blank with one of the following: horizontal, vertical. The graph of \(\frac{1}{4} f(x)\) is obtained by a __________ compression of the graph of \(f(x)\) by a factor of \(\frac{1}{4}\).

Identify the quadrant in which each point lies. $$ (-2,6) $$

Determine the quadrant where the terminal side of the given angle lies. $$75^{\circ}$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$f(x)=\sec \left(x-\frac{\pi}{2}\right)$$

Find exact values of the given trigonometric functions without the use of a calculator. $$\arctan 0$$

Use your knowledge of vertical translations to graph at least two cycles of the given functions. $$f(x)=\cos x+3$$

Sketch the angles in standard position. $$135^{\circ}$$

Skills This set of exercises will reinforce the skills illustrated in this section. In Exercises \(9-22,\) find the reference angle for each of the angles given. $$\frac{7 \pi}{6}$$

Use your knowledge of horizontal translations to graph at least two cycles of the given functions. $$f(x)=\csc \left(x+\frac{\pi}{3}\right)$$