 8.1: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.1: Use Figure 8.12 to find the following exactly: (a) tan (b) sin (c) ...
 8.8.2.1: In Exercises 12, solve for . 6 10018
 8.8.3.1: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.2: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.2: Using Figure 8.13, find exactly: (a) sin (b) sin (c) cos (d) cos (e...
 8.8.2.2: In Exercises 12, solve for . 352
 8.8.3.2: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.3: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.3: In Exercises 36, find (a) sin (b) cos 1024 2
 8.8.2.3: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.3: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.4: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.4: In Exercises 36, find (a) sin (b) cos 69117
 8.8.2.4: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.4: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.5: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.5: In Exercises 36, find (a) sin (b) cos 0.10.2
 8.8.2.5: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.5: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.6: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.6: In Exercises 36, find (a) sin (b) cos 23
 8.8.2.6: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.6: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.8.3.7: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.7: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.7: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.7: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.8: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.8: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.8: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.8: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.9: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.9: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.9: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.9: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.10: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.10: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.10: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.10: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.11: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.11: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.11: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.11: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.12: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.12: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.12: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.12: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.13: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.13: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.13: For Exercises 1318, find , an angle in a right triangle. sin = 0.876
 8.8.2.13: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.14: Convert the Cartesian coordinates in 1418 to polar coordinates. (1, 1)
 8.14: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.14: For Exercises 1318, find , an angle in a right triangle. cos = 0.016
 8.8.2.14: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.15: Convert the Cartesian coordinates in 1418 to polar coordinates. (1, 0)
 8.15: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.15: For Exercises 1318, find , an angle in a right triangle. tan = 0.123
 8.8.2.15: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.16: Convert the Cartesian coordinates in 1418 to polar coordinates. (6,2)
 8.16: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.16: For Exercises 1318, find , an angle in a right triangle. tan = 54.169
 8.8.2.16: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.17: Convert the Cartesian coordinates in 1418 to polar coordinates. (3, 1)
 8.17: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.17: For Exercises 1318, find , an angle in a right triangle. sin = 0.999
 8.8.2.17: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.18: Convert the Cartesian coordinates in 1418 to polar coordinates. (3,...
 8.18: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.18: For Exercises 1318, find , an angle in a right triangle. cos = 0.999
 8.8.2.18: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.19: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.19: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.19: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.19: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.20: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.20: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.20: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.20: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.21: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.21: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.21: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.21: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.22: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.22: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.22: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.22: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.23: Convert the equations in 2326 to rectangular coordinates. = 2
 8.23: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.23: Use Figure 8.15 to explain why, for between 0 and 90, the unit circ...
 8.8.2.23: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.24: Convert the equations in 2326 to rectangular coordinates. = 6 cos
 8.24: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.24: Using the definition of the trigonometric functions in terms of the...
 8.8.2.24: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.25: Convert the equations in 2326 to rectangular coordinates. = 4
 8.25: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.25: Figure 8.16 shows a 454590 right triangle with side and hypotenus...
 8.8.2.25: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.26: Convert the equations in 2326 to rectangular coordinates. tan = cos 2
 8.26: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.26: Figure 8.17 shows an equilateral triangle with side 2 and altitude ...
 8.8.2.26: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.27: Convert the equations in 2730 to polar coordinates. Express your an...
 8.27: You have been asked to build a ramp for Dans Daredevil Motorcycle J...
 8.8.1.27: The top of a 200foot vertical tower is to be anchored by cables th...
 8.8.2.27: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.28: Convert the equations in 2730 to polar coordinates. Express your an...
 8.28: Find the value of the angle in Figure 8.63. 52 25 63 Figure 8.63
 8.8.1.28: A surveyor must measure the distance between the two banks of a str...
 8.8.2.28: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.29: Convert the equations in 2730 to polar coordinates. Express your an...
 8.29: A ship spots a second ship to its east at a distance of four miles....
 8.8.1.29: A search and rescue volunteer leaves a rendezvous point in the Ariz...
 8.8.2.29: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.30: Convert the equations in 2730 to polar coordinates. Express your an...
 8.30: The ground crew for a hot air balloon is positioned 200 meters from...
 8.8.1.30: In 3033, a line passing through the origin and the given point form...
 8.8.2.30: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.31: For 3138, the origin is at the center of a clock, with the positive...
 8.31: A UFO is first sighted at a point 1 due east from an observer at an...
 8.8.1.31: In 3033, a line passing through the origin and the given point form...
 8.8.2.31: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.32: For 3138, the origin is at the center of a clock, with the positive...
 8.32: A kite flier wondered how high her kite was flying. She used a prot...
 8.8.1.32: In 3033, a line passing through the origin and the given point form...
 8.8.2.32: (a) Find an expression for sin in Figure 8.35 and sin in Figure 8.3...
 8.8.3.33: For 3138, the origin is at the center of a clock, with the positive...
 8.33: Hampton is a small town on a straight stretch of coastline running ...
 8.8.1.33: In 3033, a line passing through the origin and the given point form...
 8.8.2.33: In Figure 8.37: (a) Find sin (b) Solve for (c) Find the area of the...
 8.8.3.34: For 3138, the origin is at the center of a clock, with the positive...
 8.34: For each of the following expressions, find a line segment in Figur...
 8.8.1.34: A 240ft tree casts a 130foot shadow on horizontal ground. A girl ...
 8.8.2.34: Two fire stations are located 56.7 miles apart, at points and . The...
 8.8.3.35: For 3138, the origin is at the center of a clock, with the positive...
 8.35: Find tan exactly if sin = 35, and is in the fourth quadrant.
 8.8.1.35: A plane is flying at an elevation of 35,000 feet when the Gateway A...
 8.8.2.35: To measure the height of the Eiffel Tower in Paris, a person stands...
 8.8.3.36: For 3138, the origin is at the center of a clock, with the positive...
 8.36: Find the radian value of in Figure 8.68. 0.83 1 Figure 8.68
 8.8.1.36: A bridge over a river was damaged in an earthquake and you are call...
 8.8.2.36: Two airplanes leave Kennedy airport in New York at 11 am. The air t...
 8.8.3.37: For 3138, the origin is at the center of a clock, with the positive...
 8.37: (a) Explain why = 2 cos and ( 1)2 + 2 = 1 are equations for the sam...
 8.8.1.37: You want to build a wheelchair ramp leading up to your house. Your ...
 8.8.2.37: A parcel of land is in the shape of an isosceles triangle. The base...
 8.8.3.38: For 3138, the origin is at the center of a clock, with the positive...
 8.8.1.38: The pitch of a roof is the slope of a roof expressed as the ratio o...
 8.8.2.38: In video games, images are drawn on the screen using coordinates. ...
 8.8.3.39: In 3941, give inequalities for and that describe the following regi...
 8.8.1.39: Find approximately the acute angle formed by the line = 2 + 5 and t...
 8.8.2.39: A computergenerated image begins at screen coordinates (5, 3). The...
 8.8.3.40: In 3941, give inequalities for and that describe the following regi...
 8.8.1.40: (a) Find expressions in terms of , , and for the sine, cosine, and ...
 8.8.2.40: Derive the Law of Cosines assuming the angle is obtuse, as in Figur...
 8.8.3.41: In 3941, give inequalities for and that describe the following regi...
 8.8.1.41: Knowing the height of the Columbia Tower in Seattle, determine the ...
 8.8.2.41: Use Figure 8.39 to show that sin = sin . Figure 8.39
 8.8.3.42: (a) Make a table of values for the equation = 1 sin . Include = 0, ...
 8.8.1.42: A tree 50 feet tall casts a shadow 60 feet long. Find the angle of ...
 8.8.2.42: In baseball, the four bases form a square. The pitcher stands near ...
 8.8.3.43: Graph the equation = 1 sin(), for = 1, 2, 3, 4. What is the relatio...
 8.8.1.43: A staircase is to rise 17.3 feet over a horizontal distance of 10 f...
 8.8.2.43: A park director wants to build a bridge across a river to a bird sa...
 8.8.3.44: Graph the equation = 1 sin , with 0 , for = 2, 3, 4. What is the re...
 8.8.1.44: (a) In the right triangle in Figure 8.23, angle = 30 and = 2 3. Fin...
 8.8.2.44: To estimate the width of an archaeological mound, archaeologists pl...
 8.8.3.45: Graph the equation =1 sin , for = 2, 3, 4. What is the relationship...
 8.8.1.45: To check the calibration of their transit (an instrument to measure...
 8.8.2.45: Every triangle has three sides and three angles. Make a chart showi...
 8.8.3.46: Graph the equation = 1cos . Describe its relationship to = 1 sin .
 8.8.1.46: A ladder 3 meters long leans against a house, making an angle with ...
 8.8.2.46: The telephone company needs to run a wire from the telephone pole a...
 8.8.3.47: Give inequalities that describe the flat surface of a washer that i...
 8.8.1.47: You are parasailing on a rope that is 125 feet long behind a boat. ...
 8.8.2.47: A buyer is interested in purchasing the triangular lot with vertice...
 8.8.3.48: Graph the equation = 1 sin(2) for 0 2. There are two loops. For eac...
 8.8.2.48: Solve the following triangles for and . 40 8 7 (a) Figure 8.45 40 8...
 8.8.3.49: A slice of pizza is one eighth of a circle of radius 1 foot. The sl...
 8.8.2.49: A triangle has angles 23, 5, and 215. The length of the side opposi...
 8.8.3.50: A radio tower located on the coast can be configured to transmit mo...
 8.8.3.51: A superdirectional microphone, also called shotgun microphone,6 is...
Solutions for Chapter 8: Functions Modeling Change: A Preparation for Calculus 5th Edition
Full solutions for Functions Modeling Change: A Preparation for Calculus  5th Edition
ISBN: 9781118583197
Solutions for Chapter 8
Get Full SolutionsChapter 8 includes 184 full stepbystep solutions. Since 184 problems in chapter 8 have been answered, more than 18917 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Functions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9781118583197. This textbook survival guide was created for the textbook: Functions Modeling Change: A Preparation for Calculus, edition: 5.

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

Cycloid
The graph of the parametric equations

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Differentiable at x = a
ƒ'(a) exists

Domain of validity of an identity
The set of values of the variable for which both sides of the identity are defined

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Explanatory variable
A variable that affects a response variable.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Identity properties
a + 0 = a, a ? 1 = a

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Multiplicative inverse of a matrix
See Inverse of a matrix

Obtuse triangle
A triangle in which one angle is greater than 90°.

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the xaxis, and a perpendicular dropped from a point on the terminal side to the xaxis. The angle in a reference triangle at the origin is the reference angle

Reflexive property of equality
a = a

Scatter plot
A plot of all the ordered pairs of a twovariable data set on a coordinate plane.