Solution manual for trigonometry 2nd edition by stewart

a To find the x -intercepts of the graph of an equation we set y equal to in the equation and solve for Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Editi

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Trigonometry, 2e 1

Chapter 1 Fundamentals

1.1 Coordinate Geometry

1 The point that is 3units to the right of the y-axis and 5units below the x-axis has coordinates 3, 5

2 The distance between the points a b , and c d , is 2

c a d b 2 So the distance between

4 If the point 2, 3 is on the graph of an equation in and y , then the equation is satisfied when we replace

by and y by 3 We check whether

is not on the graph of the equation 2 y x 1

5 (a) To find the x -intercept(s) of the graph of an equation we set y equal to in the equation and solve for

Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart

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2 Chapter 1: Functions and Graphs

10 The two points are 2, 1 and 2,2

NOT FOR SALE nctions and Graphs nctions and Gra

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20 The area of a parallelogram is its base times its height Since two sides are parallel to the x -axis, we use the

length of one of these as the base Thus, the base is d A , B  (1 5)2 (2 2 )2 ( 4) 2 4 The height is the change in the y coordinates, thus, the height is 6 2 So the area of the parallelogram

b d C D ; and h is the difference in y -coordinates is

3 0 3 Thus the area of the trapezoid is 4 2

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and CB have the same length

38 Since the side AB is parallel to the x -axis, we use this as the base in the formula area

¢ , ± ¢ d C B , ± ¢ , ¯ ±2 , we conclude that the triangle is a right triangle

(b) The area of the triangle is 1 1

2¸ d C B , ¸ d A B , ¸2 10 2 10 ¸ 10

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d A B d B C d A C , , and the points are collinear

43 Let P  0, y be such a point Setting the distances equal we get

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a d A Aa  , 11 2

2

145 0

2

45 As indicated by Example 3, we must find a point S x y 1, 1 such that the midpoints of PR and of QS

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1, :

? 2 1

2 1 1 ¯ 1

? 1

2 1 ¯

? 1

2 2 1 Yes

NOT FOR SALE unctions and Graphs unctions and Gr

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2 , are all points on the graph of this equation

53 To find x -intercepts, set This gives 0 or

, so the -intercept are 0 and 4 To find y -intercepts, set This gives

, so the -intercept are and

To find y -intercepts, set This gives

2 9

x 3

55 To find x -intercepts, set y  0 This gives x4 02 x 0 16

So the x -intercept are and 2

To find y -intercepts, set This gives

4 16

x 2

0

x  04 y2 0 y 16 So the y -intercept are and

2 16

y  4

So the x -intercept are and 8

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4

82

When y we get So the

-intercept is 4 , and º y , so the

-intercept is

x -axis symmetry:

, which is not the same as , so the graph is not symmetric with respect to the x -axis

4

y x

4

y x , which is not the same as , so the graph is not symmetric with respect to the y -axis

Origin symmetry:

4

, which is not the same as , so the graph is not symmetric with respect to the origin

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intercept is 3 When we get

, which is not the same, so the graph

is not symmetric with respect to the x -axis

y -axis symmetry:

3

x y

, which is not the same as , so the graph is not symmetric with respect to the y -axis

3

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x

2

x x

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y 2

4x y

, which is not the same as y 14x2 ,

so the graph is not symmetric with respect to the

01

3 1 8

y x , so the graph is not symmetric with respect to the y -axis

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symmetric with respect to the x -axis

y

29

9

y

9

y

2

Z

Y

M

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y -axis symmetry:

2

4

y 2 , so the y -intercept is Since

we are graphing real numbers and

2 4

defined to be a nonnegative number, the equation is not symmetric with respect to the x -axis nor with respect to the y -axis Also, the equation is not symmetric with respect to the origin

Z

M

Y

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69. y  4  x2 Since the radicand (the inside

of the square root) cannot be negative, we must have

y p

-intercept is 2 Since , the graph is not

symmetric with respect to the x -axis

y -axis symmetry:

24

y x 4 x2

0

y p

, so the graph is symmetric with respect to the y -axis Also, since

the graph is not symmetric with respect to the origin

Z

Y

M

70 Since the radicand (the expression inside the

square root symbol) cannot be negative, we must have 4 x2 p 0 x b2 4 2

graph is symmetric with respect to the y -axis

Origin symmetry: Since , the graph is not symmetric with respect to the origin

Z

Y

M

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72 Since is solved for x in terms of y

, we insert values for y and find the corresponding values of x

is not the same as , so the graph is not symmetric with respect to the x -axis

, so the graph is symmetric with respect to the origin

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16

y

416

16

y

416

-y

0 p

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y x , so the graph is not symmetric with

respect to the x -axis

y x , so the graph is not symmetric with

respect to the origin

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so the graph is not symmetric with respect to the x -axis

y -axis symmetry: y x , so the graph is symmetric with respect to the y

-axis

, so the graph is not symmetric with respect to the origin

, so the graph is not symmetric with respect to the x -axis

, so the graph is not symmetric with respect to the y -axis

with respect to the origin

2 2

x y xy 1

80. x -axis symmetry: x4 y 4 x2 y 2 1 , so the graph is symmetric

with respect to the x -axis

with respect to the y -axis

, so the graph is not symmetric with respect to the x -axis

, so the graph is not symmetric with respect to the y -axis

graph is symmetric with respect to the origin

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Trigonometry, 2e 23

82. x -axis symmetry: y x2 x y x2  x , which is not the same as

2

y x x , so the graph is not symmetric with respect to the x -axis

y -axis symmetry: y x 2 x y x2 x , so the graph is symmetric with respect to the

-axis Note that

y x x

Origin symmetry: y x 2 x y x2 x y x2  x , which is not

the same as y x2 x , so the graph is not symmetric with respect to the origin

84 Symmetric with respect to the x -axis

88. x2 y2 5 has center 0, 0 and radius

5

Z Z

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, we solve for This gives

Thus, an equation of the circle is

2

r

4 1 2 6 5 2 r2

y

Full file at https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 2nd- Edition- by- Stewart< /h3>

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Full file at https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 2nd- Edition- by- Stewart< /h3>

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