Precalculus Midterm 2

Question 1

Properties of Natural Logarithms

Answer 1

Question 2

the Natural Logarithmic function is the inverse of the natural exponential function

Answer 2

Question 3

Graph of the Natural Logarithmic Function

Answer 3

Question 4

Natural Logarithms

Answer 4

Question 5

Common Logarithms

Answer 5

Question 6

Graph of the Family of Logarithmic Functions

Answer 6

Question 7

Graphing a Logarithmic Function by Plotting Points

Answer 7

Question 8

Inverse Function Property Domain

Answer 8

Question 9

Inverse Property Function

Answer 9

Question 10

Log to Exponential Form

Answer 10

Question 11

Omitting the Parenthesis

Answer 11

Question 12

Definition of the Logarithmic Function

Answer 12

Question 13

4.3 Definition of Logarithmic Functions

video

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp60403a&title=Logarithmic%20Functions%20I

Answer 13

Question 14

Since Logarithms arw exponents the Laws of Exponents give Rise to the Laws of Logarithms

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp60404&title=Laws%20of%20Logarithms

Answer 14

Question 15

Expanding and Combining Logarithmic Expressions

PG 355

Answer 15

Question 16

WARNING There is no corresponding Logarithm Rule for of a Sum or a Difference

pg 356

Answer 16

Question 17

Change of Base Formula Explanation

pg 357

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp70404&title=Change%20of%20Base%20Formula

Answer 17

Question 18

Another Way to Look at the Change of Base Formula

pg 357

Answer 18

Question 19

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp60405&title=Exponential%20Equations

Answer 19

Question 20

4.5 Guidlines for Solving Exponential Equations

Answer 20

Question 21

Solving an Exponential Equation by isolating the exponential term

Answer 21

Question 22

When x is on both sides of the exponent

Answer 22

Question 23

When x is in the denominator of an exponential equation

Answer 23

Question 24

When an exponential equation is a quadratic equation

It must be factored

Answer 24

Question 25

4.5 When the **Exponential Equation** has A **Common Factor**

Answer 25

Question 26

4.5 Solve the **Logarithmic Equation** for x

Answer 26

Question 27

4.5 Using the Quadratic Equation to Solve a Logarithmic Equation

Answer 27

Question 28

4. 5 Exponential Equation Inequality https: //www.webassign.net/v4cgi/extra/bc\_enhanced/index.tpl?asset=watch\_it\_player&asset\_url=/bc\_enhanced/sprecalc7\_w\_player/scolalg5\_05\_04\_070.html&UserPass=40416dd1f85ab2d92f82bfef24bd5be5

Answer 28

Question 29

http://college.cengage.com/mathematics/blackboard/shared/content/video\_explanations/video\_wrapper.html?filename=kazmierczak/srwp70405&title=Compound%Interest

Answer 29

Question 30

get it from book problems pdf

Question 32

Positive and Negative Angles are determined by the movement of the terminal side away from the initial side clockwise-**negative** **counter** clockwise-**positive**

Answer 32

Question 33

How Radians (the preferred angle measure in calculus) are measured

Answer 33

Note the arc created by the line is the same length as the line or 1 radian

Question 34

6. 1 Converting between Radians and Degrees https: //www.webassign.net/v4cgi/extra/bc\_enhanced/index.tpl?asset=watch\_it\_player&asset\_url=/bc\_enhanced/sprecalc7\_w\_player/sprecalc6\_06\_01\_005.html&UserPass=bd5ee596620b98562a811b6665bca489 and https://www.webassign.net/v4cgi/extra/bc\_enhanced/index.tpl?asset=watch\_it\_player&asset\_url=/bc\_enhanced/sprecalc7\_w\_player/sprecalc6\_06\_01\_017.html&UserPass=bd5ee596620b98562a811b6665bca489

Answer 34

Question 35

Angles in standard position all start **(initial side)** on the positive x axis

Answer 35

Question 36

Coterminal Angles-have the same initial and terminal sides just have more rotations of 360° or 2π https://www.webassign.net/v4cgi/extra/bc\_enhanced/index.tpl?asset=watch\_it\_player&asset\_url=/bc\_enhanced/sprecalc7\_w\_player/sprecalc6\_06\_01\_035.html&UserPass=bd5ee596620b98562a811b6665bca489

Answer 36

**Positive** Coterminal Angles **add multiples** of **360°** or **2π** **Negative** Coterminal Angles **subtract multiples** of **360°** or **2π**

Question 37

Interactive Unit Circle

Answer 37

https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html

Question 38

The Unit Circle Cosine,Sine

Answer 38

Question 39

Trigonometry of right Triangles- **The Special Two Triangles to Remember** http://college.cengage.com/mathematics/blackboard/shared/content/video\_explanations/video\_wrapper.html?filename=kazmierczak/srwp70602&title=Trigonometric%20Ratios%20and%20Special%20Triangles

Answer 39

Question 40

The Trigonomic Ratios to Remember

Answer 40

Question 41

SOHCAHTOA

Answer 41

Question 42

The **Reciprocal** Relations in Trig ## Footnote **Cosecant** **Secant** **Cotangent**

Answer 42

Question 43

**Height of a Building** Angle of **Elevation** Angle of **Depression** **Line of Sight**

Answer 43

Question 44

Height of a Tree

Answer 44

Question 45

Fundemental Identities of Trig

Answer 45

Question 46

Definition of Trigonomic Functions

Answer 46

Question 47

All Students Take Calculus

Answer 47

All Students Take Calculus

Question 48

see page 494

Question 49

Periodic Properties of Sine and Cosine Sine of t or Cosine of t remain the same as you ad 2∏ periods

Answer 49

Question 50

Graph of the unit circle values http://college.cengage.com/mathematics/precalculus/animations/stewart/sp060503f02.html

Answer 50

Note the color pattern as the circle stretches along the line as one period of 2∏

Question 51

One period of y=sin t 0≤ *t* ≤2∏

Answer 51

Graph of sin *t for* 0≤ *t* ≤2∏

Question 52

One period of x=cosine t 0≤ *t* ≤2∏

Answer 52

Graph of cos t for 0≤ *t* ≤ 2∏

Question 53

**Vertical** transformaton of Cosine Curve

Answer 53

**Vertical** transformaton of Cosine Curve by +2

Question 54

5.3 Reflection of a Cosine Curve

Answer 54

Reflction of a cosine curve -cos

Question 55

Vertical **Stretching** and **Shrinking** of a Sin Graph **AMPLITUDE is the true Value of the number in front of the sin or cos** **⎢a⎥sin**

Answer 55

The Higher the number the higher the peaks y=2 sin x Fractions cause Flatter Graphs y=1/2 sin x

Question 56

Finding the Period of Sine and Cosine Curves period=2∏/k

Answer 56

Question 57

https://www.webassign.net/v4cgi/extra/bc\_enhanced/index.tpl?asset=watch\_it\_player&asset\_url=/bc\_enhanced/sprecalc7\_w\_player/sprecalc6\_05\_03\_043.html&UserPass=44b63ef21500978162e459f571f147ab

Answer 57

From the graph the period =2π so 2π/**k**=2π **k**=1

Question 58

Horizontal Shift on a Graph ## Footnote Remember it is the part (x-b) and is a shift in an **Unexpected Direction** this affects x so it is in the parenthesis with x

Answer 58

Question 59

Inverse Sine Function

Answer 59

Question 60

Inverse Cosine Function

Answer 60

Question 61

Inverse Tangent Function

Answer 61

Question 62

Periodic Properties of tan cot sec csc

Answer 62

Question 63

Tangent Graph crosses the origin and swings to the right

Answer 63

Question 64

The Cotangent graph does not cross the origin and swigs to the left

Answer 64

Question 65

The secant graph has a period of 2π and looks like a U straddling the y axis

Answer 65

Question 66

The Cosecant Graph looks like a U between 0 and π in the first quadrant with a period of π and is an upside down U in quadrant 2

Answer 66

Question 67

Tangent and Cotangent figuring the period π/k

Answer 67

Question 68

The secant and cosecant period is 2π/k

Answer 68

Question 69

Reciprical identities Pythagorean Identities Even odd Identities Cofunction Identities

Answer 69

Question 70

Addition and Subtraction Formulas

Answer 70

Question 71

Double Angle Formulas

Answer 71