By using a graphing utility to complete the following table.Round your answer to four decimal places. \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ \hline y _ { 2 } & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \cdots \\ \hline \end{array}\] $y _ { 1 } = \frac { \cos x } { 1 - \sin x } , y _ { 2 } = \frac { 1 + \sin x } { \cos x }$

A) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & 2.4650 & 3.4082 & 5.3319 & - 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & 2.4650 & 3.4082 & 5.3319 & - 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] B) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & - 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & - 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] C) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] D) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & 2.4650 & 3.4082 & - 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & 2.4650 & 3.4082 & - 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] E) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] A) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & 2.4650 & 3.4082 & 5.3319 & - 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & 2.4650 & 3.4082 & 5.3319 & - 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] B) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & - 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & - 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] C) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] D) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & 2.4650 & 3.4082 & - 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & 2.4650 & 3.4082 & - 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] E) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.8 & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\ \hline y _ { 1 } & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline y _ { 2 } & 2.4650 & 3.4082 & 5.3319 & 11.6814 & - 68.4797 & - 8.6876 & - 4.5880 \\ \hline \end{array}\] E

By using a graphing utility to complete the following table.Round your answer to two decimal places. \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & - & - & - & - & - & - & - \\ \hline y _ { 2 } & - & - & - & - & - & - & - \\ \hline \end{array}\] $y _ { 1 } = \sec ^ { 4 } x - \sec ^ { 2 } x , y _ { 2 } = \tan ^ { 2 } x \sec ^ { 2 } x$

A) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & - 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & - 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] B) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] C) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & 0.69 & - 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & 0.69 & - 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] D) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & - 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & - 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] E) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & - 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & - 1,163.61 \\ \hline \end{array}\] A) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & - 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & - 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] B) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] C) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & 0.69 & - 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & 0.69 & - 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] D) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & - 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & - 0.69 & 2.18 & 8.31 & 50.39 & 1,163.61 \\ \hline \end{array}\] E) \[\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & 0.2 & 0.4 & 0.6 & 0.8 & 1 & 1.2 & 1.4 \\ \hline y _ { 1 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & - 1,163.61 \\ \hline y _ { 2 } & 0.04 & 0.21 & 0.69 & 2.18 & 8.31 & 50.39 & - 1,163.61 \\ \hline \end{array}\]

Exam 31: Using Fundamental Identities

By using a graphing utility to complete the following table.Round your answer to four decimal places. x 0.8 1.0 1.2 1.4 1.6 1.8 2.0 \@cdots \@cdots \@cdots \@cdots \@cdots \@cdots \@cdots \ldots \ldots \ldots \ldots \ldots \ldots \@cdots $y _ { 1 } = \frac { \cos x } { 1 - \sin x } , y _ { 2 } = \frac { 1 + \sin x } { \cos x }$

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

E

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where $0 < \theta < \frac { \pi } { 2 }$ . $\sqrt { 11 - x ^ { 2 } } , x = \sqrt { 11 } \sin \theta$

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(Multiple Choice)

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Question 2

Correct Answer:

Verified

B

Find the rate of change of the function $f ( x ) = - \csc x - \cos x$ .

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(Multiple Choice)

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(Multiple Choice)

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Question 13

The forces acting on an object weighing W units on an inclined plane positioned at an angle of θ with the horizontal (see figure)are modeled by $\mu W \sin \theta = W \tan \theta$ where μ is the coefficient of friction.Solve the equation for μ and simplify the result. $The forces acting on an object weighing W units on an inclined plane positioned at an angle of θ with the horizontal (see figure)are modeled by \mu W \sin \theta = W \tan \theta where μ is the coefficient of friction.Solve the equation for μ and simplify the result. $

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Question 20

Exam 31: Using Fundamental Identities

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where 0<θ<π20 < \theta < \frac { \pi } { 2 }0<θ<2π​ . 11−x2,x=11sin⁡θ\sqrt { 11 - x ^ { 2 } } , x = \sqrt { 11 } \sin \theta11−x2​,x=11​sinθ ​

Find the rate of change of the function f(x)=−csc⁡x−cos⁡xf ( x ) = - \csc x - \cos xf(x)=−cscx−cosx . ​

Which of the following is equivalent to the given expression? cos⁡2x1+sin⁡x\frac { \cos ^ { 2 } x } { 1 + \sin x }1+sinxcos2x​ ​

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.​ sin⁡3x−sin⁡2x−sin⁡x+1\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1sin3x−sin2x−sinx+1 ​

Rewrite ln⁡∣sin⁡θ∣−ln⁡∣cos⁡θ∣\ln | \sin \theta | - \ln | \cos \theta |ln∣sinθ∣−ln∣cosθ∣ as a single logarithm and then simplify the result. ​

Rewrite ln⁡∣sec⁡θ∣+ln⁡∣sin⁡θ∣\ln | \sec \theta | + \ln | \sin \theta |ln∣secθ∣+ln∣sinθ∣ as a single logarithm and then simplify the result.

Use the given values to evaluate (if possible)three trigonometric functions sin x,cos x,cot x.​ csc⁡x=419,tan⁡x=940\csc x = \frac { 41 } { 9 } , \tan x = \frac { 9 } { 40 }cscx=941​,tanx=409​ ​

If x = 2 tan θ,use trigonometric substitution to write 4+x2\sqrt { 4 + x ^ { 2 } }4+x2​ as a trigonometric function of θ,where −π2<θ<π2- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }−2π​<θ<2π​ . ​

If x = 2 tan θ,use trigonometric substitution to write 4+x2\sqrt { 4 + x ^ { 2 } }4+x2​ as a trigonometric function of θ,where 0<θ<π20 < \theta < \frac { \pi } { 2 }0<θ<2π​ . ​

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression. csc⁡x−sin⁡xcot⁡x\frac { \csc x - \sin x } { \cot x }cotxcscx−sinx​

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where 0<x<π20 < x < \frac { \pi } { 2 }0<x<2π​ . x2+25,x=5tan⁡θ\sqrt { x ^ { 2 } + 25 } , x = 5 \tan \thetax2+25​,x=5tanθ ​

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. ​​ cot⁡2α+cot⁡2α⋅tan⁡2α\cot ^ { 2 } \alpha + \cot ^ { 2 } \alpha \cdot \tan ^ { 2 } \alphacot2α+cot2α⋅tan2α

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. sin⁡3x−sin⁡2x−sin⁡x+1\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1sin3x−sin2x−sinx+1 ​

Use the fundamental identities to simplify the expression. ​ Cot θ sec θ ​

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. sin⁡(π2−x)csc⁡x\sin \left( \frac { \pi } { 2 } - x \right) \csc xsin(2π​−x)cscx

Use the given values to evaluate (if possible)three trigonometric functions cos x,csc x,tan x.​ sec⁡x=3,sin⁡x=−63\sec x = \sqrt { 3 } , \sin x = - \frac { \sqrt { 6 } } { 3 }secx=3​,sinx=−36​​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where $0 < \theta < \frac { \pi } { 2 }$ . $\sqrt { 11 - x ^ { 2 } } , x = \sqrt { 11 } \sin \theta$

Find the rate of change of the function $f ( x ) = - \csc x - \cos x$ .

Which of the following is equivalent to the given expression? $\frac { \cos ^ { 2 } x } { 1 + \sin x }$

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$

Rewrite $\ln | \sin \theta | - \ln | \cos \theta |$ as a single logarithm and then simplify the result.

Rewrite $\ln | \sec \theta | + \ln | \sin \theta |$ as a single logarithm and then simplify the result.

Use the given values to evaluate (if possible)three trigonometric functions sin x,cos x,cot x. $\csc x = \frac { 41 } { 9 } , \tan x = \frac { 9 } { 40 }$

If x = 2 tan θ,use trigonometric substitution to write $\sqrt { 4 + x ^ { 2 } }$ as a trigonometric function of θ,where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .

If x = 2 tan θ,use trigonometric substitution to write $\sqrt { 4 + x ^ { 2 } }$ as a trigonometric function of θ,where $0 < \theta < \frac { \pi } { 2 }$ .

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression. $\frac { \csc x - \sin x } { \cot x }$

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where $0 < x < \frac { \pi } { 2 }$ . $\sqrt { x ^ { 2 } + 25 } , x = 5 \tan \theta$

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\cot ^ { 2 } \alpha + \cot ^ { 2 } \alpha \cdot \tan ^ { 2 } \alpha$

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$

Use the fundamental identities to simplify the expression. Cot θ sec θ

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$

Use the given values to evaluate (if possible)three trigonometric functions cos x,csc x,tan x. $\sec x = \sqrt { 3 } , \sin x = - \frac { \sqrt { 6 } } { 3 }$