Download Trig. Review Sheet P.1-P.4 Answers

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Trigonometry
Chapter 1 Review Sheet (1.1-1.4&1.6)
Put the following into interval notation. Then describe it as bounded or unbounded.
Interval notation
Bounded or unbounded?
x<3
unbounded
(-, 3)
[-2,9]
bounded
x  -22
[-22,)
unbounded
-12 < x < -2
(-12, -2)
bounded
0 < x  15
(0, 15]
bounded
-2  4  9
What makes an interval bounded?
If the interval has an endpoint on each end, it is bounded.
What makes an interval unbounded?
If the interval continues without end it is unbounded. In other
words, the interval contains an  symbol.
Describe when you use ( ) or [ ] in interval notation.
You use parentheses for < and >. You use brackets for  and
.
Define the following:
Rational number –
Any number that can be expressed as a fraction.
Integer –
Any number that can be expressed as a fraction with a
denominator of 1.
Whole number –
Positive integers and zero. Example: 0, 1, 2, 3, …
Natural number-
Counting numbers. Example: 1, 2, 3, 4, 5,… (Whole numbers
except for zero.)
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 1 of 8
Categorize the following numbers as rational, irrational, integer, whole numbers, counting
numbers. Remember, some numbers may fall in more than one category.
13, -2.45, -e, 121/4, -8, 2, 16, 0, 5.111, -4.353353335...,  14, 3 2,
Rational Numbers:
Irrational Numbers:
Integers:
13, 16, 0,
/3, 6
13, -8, 16, 0,
6
13, -2.45, 121/4, -8, -e, 2,
16, 0, 5.111, 12/3, -4.353353335...,
6
 14, 3 2
Whole Numbers:
12
12
/3,
Counting Numbers:
12
/3, 6
13, 16,
12
/ 3, 6
What are four possible methods of solving quadratic equations?
Quadratic Formula, Completing the Square, Extracting Roots,
Factoring/Zero Product Property
What is the difference between an identity and a conditional equation?
An identity has infinitely many solutions (any real number you
can think of is a solution). A conditional equation has a limited
number of solutions.
When solving what kind of equations must you check your answers for extraneous solutions?
Rational Equations, Absolute Value equations and Radical
Equations
Solve the following equations. Be sure to check for extraneous solutions. There may be
problems that are identities and there may be problems with no solution. If that is the case,
write IDENTITY or NO SOLUTION.
3(x + 3) = 5(1 – x) – 1
(x+2)2 + 4 = (x + 3)2
x = -5/8
x2 + 2(3x – 2) = x2 + 6x – 4
x = -1/2
100 – 4x = 5x + 6 + 6
3
4
x = all real numbers
(Identity)
x = 10
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 2 of 8
10x + 3 = 1
5x + 6
2
6 - 2
= 3(x + 5)
x
x+3
x2 + 3x
x=0
x = -3
x2 – 2x – 8 = 0
(x + 3)2 = 81
x = 4 or x = -2
x = 6 or x = -12
x + 2 = x
(x – 2)2= x2 – 4
x=2
x = 2 , x = -1
4x4 – 18x2 = 0
| x + 1 | = x2 + x
x=1
x = 0, x = 32/2
Write out the following formulas:
Distance formula:
Midpoint formula:
x 1 + x 2 , y1 + y 2
d =  (x2 – x1) 2 + (y2 – y1)2
2
Slope formula:
m=
y2 – y 1
x2 - x 1
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 3 of 8
2
Determine the distance, midpoint and slope of the line segment that connects the following
two points. Be sure to simplify all fractions and all radicals.
Distance:
Midpoint:
Slope:
(6,5) & (-8,3)
102
(-1,4)
82
(1.9, 1.4)
1
/7
(-2.1, 5.4) & (5.9, -2.6)
-1
Fill in the missing sections of the chart below regarding circles:
Center
Radius
Standard Form:
General Form:
2
2
2
2
(x – h) + (y – k) = r
Ax +By2+Cx+Dy+E = 0
(2,3)
1
(x – 2)2 + (y – 3)2 = 1
x2 + y2 - 4x - 6y + 12 = 0
(-2,0)
5
(x + 2)2 + (y – 0)2 = 25
x2 + y2 + 4x - 21 = 0
(x – 2)2 + (y + 3)2 = 8
x2 + y2 - 4x + 6y + 5 = 0
/3
(x -1/2)2 + (y + 3/8)2 = 1/9
576x2 +576 y2 - 576x + 432y - 79 = 0
(3, -6)
311
(x – 3)2 + (y + 6)2 = 99
x2+y2-6x+12y-54 = 0
(0,5)
41
x2 + (y - 5)2 = 41
2x2+2y2-20y-32=0
(2, -3)
(1/2, -3/8)
22
1
Fill in all information below for the circle whose diameter is
the line segment between (-2,2) and (4,-10)
(1,-4)
35
2
2
(x – 1) + (y + 4) = 45
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 4 of 8
x2 + y2 - 2x + 8y - 28 = 0
Complete the following charts with the appropriate procedures on determining symmetry:
To determine
To determine
To determine
x-axis symmetry
y-axis symmetry
origin symmetry
Replace y with (-y)
Clean up
Check to see if new =
old
Replace x with (-x)
Clean up
Check to see if new =
old
Replace x with (-x)
Replace y with (-y)
Clean up
Check to see if new =
old
Determine what type of symmetry the following graphs will have (if any).
3x + 2y = 12
x-axis:
y-axis:
Origin:
3x + 2(-y) = 12
3(-x) + 2y = 12
3(-x) + 2(-y) = 12
No
No
No
y + 2x2 = 0
x-axis:
y-axis:
2
Origin:
2
(-y) + 2x = 0
y + 2(-x) = 0
(-y) + 2(-x)2 = 0
No
Yes
No
y=
x-axis:
2x
x2 – 4x
y-axis:
2x
(-y) = 2
x – 4x
Origin:
2(-x)
y= 2
(-x) – 4(-x)
2(-x)
(-y) = 2
(-x) – 4(-x)
No
No
No
y = x3
x-axis:
y-axis:
(-y) = x
3
Origin:
3
y = (-x)
(-y) = (-x)3
No
Yes
No
2y2 = x3
x-axis:
y-axis:
2
2(-y) = x
Yes
3
Origin:
2
3
2y = (-x)
2(-y)2 = (-x)3
No
No
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 5 of 8
Complete the following charts with the appropriate procedures on determining x and yintercepts:
To determine
To determine
x-intercept
y-intercept
Replace y with zero.
Replace x with zero.
Determine the x and y-intercepts of the following graphs. Be sure to write your answer as an
ordered pair (#,0) and (0,#).:
y =  25 – x2
y-intercepts:
x-intercepts:
(0) =  25 – x2
y =  25 – (0)2
(5,0) & (-5,0)
(0,5)
x2 + y2 – 12x + 20 = 0
y-intercepts:
x-intercepts:
x2 + (0)2 – 12x + 20 = 0
(0)2 + y2 – 12(0) + 20 = 0
(2,0) & (10,0)
none
xy = 7
y-intercepts:
x-intercepts:
x(0) = 7
(0)y = 7
none
none
Write equations of the various forms of linear equations:
Slope-intercept form:
Point-Slope form:
y = mx + b
Standard Form:
(y – y1) = m(x – x1)
General Form:
Ax + By = C
Ax + By + C = 0
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 6 of 8
What must you remember about the coefficients of the Standard Form and the General Form?
They must be integers. They cannot be fractions.
What does a vertical line’s equation look like? x
What is the slope of a vertical line? There
=#
is no slope.
What does a horizontal line’s equation look like? y
What is the slope of a horizontal line? Slope
=#
= 0.
Fill in the various forms of the linear equations provided the given information:
The line that has a slope of 5 and passes through (0,9)
Slope-intercept form: Point-Slope Form:
Standard Form:
General Form:
y = 5x + 9
y – 9 = 5(x – 0)
The line that passes through (2,1) and (14,6)
Slope-intercept form: Point-intercept form:
y = 5/12x + 1/6
y – 1 = 5/12(x – 2)
or
5
y – 6 = /12 (x – 14)
5x – y = -9
Standard form:
5x -12y = -2
5x – y + 9 = 0
General form:
5x -12y + 2 = 0
The line that perpendicular to y = 2/3x – 6 and passing through the point (1,-5)
Slope-intercept form: Point-Slope Form:
Standard Form:
General Form:
y = -3/2x + 13/2
y + 5 = -3/2(x – 1)
3x + 2y = 13
The vertical line passing through the point (-5,2)
Slope-intercept form: Point-Slope Form:
Standard Form:
None
None
(because there (because there
is no slope)
is no slope)
x = -5
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 7 of 8
3x + 2y – 13 = 0
General Form:
x+5=0
Graph the following. Use intercepts and symmetry as an aid in graphing. Then determine
the range and domain.
y = x2 – 2x
y = x3 + 3
y=x–3
D: [-1,)
R: (-, )
D: [3,)
R: (0, )
D: (-,)
R: (-, )
y = –| x – 6|
y = –2x – 3
x=5
D: (-, )
R: (-, 0]
D: (-,)
R: (-, )
D: x = 5
R: (-, )
x2 + y2 = 9
y = x – 5
y = -(x - 3)2 + 1
D: [-3,3]
R: [-3,3]
D: [0,)
R: [-5, )
D: (-, )
R: (-, 1]
Trigonometry
Chapter 1 Review Sheet
1.1-1.4 & 1.6
Page 8 of 8