Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \\ \hline \tan & & \frac { \pi } { 2 } & \\ \hline \end{array}\] ?

A) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 90 ^ { \circ } & \frac { \pi } { 2 } & \text { Not defined } \\ \hline \end{array}\] B) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 45 ^ { \circ } & \frac { \pi } { 2 } & 1 \\ \hline \end{array}\] C) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \\ \hline \tan & 60 ^ { \circ } & \frac { \pi } { 2 } & \sqrt { 3 } \\ \hline \end{array}\] D) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 0 ^ { \circ } & \frac { \pi } { 2 } & 0 \\ \hline \end{array}\] E) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 30 ^ { \circ } & \frac { \pi } { 2 } & \frac { \sqrt { 3 } } { 3 } \\ \hline \end{array}\] A) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 90 ^ { \circ } & \frac { \pi } { 2 } & \text { Not defined } \\ \hline \end{array}\] B) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 45 ^ { \circ } & \frac { \pi } { 2 } & 1 \\ \hline \end{array}\] C) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \\ \hline \tan & 60 ^ { \circ } & \frac { \pi } { 2 } & \sqrt { 3 } \\ \hline \end{array}\] D) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 0 ^ { \circ } & \frac { \pi } { 2 } & 0 \\ \hline \end{array}\] E) ? \[\begin{array} { | c | c | c | c | } \hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \\ \hline \tan & 30 ^ { \circ } & \frac { \pi } { 2 } & \frac { \sqrt { 3 } } { 3 } \\ \hline \end{array}\]

Exam 25: Right Triangle Trigonometry

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. sin 90° = 1,tan 90° = Not defined Sin 0° and tan 0°

(Multiple Choice)

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Question 41

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ Function \theta() \theta( rad ) Function Value ?

(Multiple Choice)

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Question 42

Using the figure below,if ? = 20° and y = 16,determine the exact value of r.

(Multiple Choice)

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Question 43

Evaluate each function.Round your answers to four decimal places.? $\cot \left( \frac { \pi } { 15 } \right)$ and $\tan \frac { \pi } { 15 }$ ?

(Multiple Choice)

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Question 44

Using the figure below,if ? = 33° and y = 9,determine the exact value of x.

(Multiple Choice)

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Question 45

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\cos \beta = \frac { \sqrt { 5 } } { 4 }$ ? $\sec \beta \text { and } \sin \left( 90 ^ { \circ } - \beta \right)$ ?

(Multiple Choice)

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Question 46

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity. ?

(Multiple Choice)

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Question 47

Find the exact value of csc ?,using the triangle shown in the figure below,if $a = 4$ and $b = 3$ .

(Multiple Choice)

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Question 48

Given $\sec \theta = \sqrt { 10 }$ and tan ? = 3,determine the following. ? Cos(90° - ?) ?

(Multiple Choice)

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Question 49

Find the exact values of the six trigonometric functions of the angle ? for the triangle. ?

(Multiple Choice)

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Question 50

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\sec \theta = 9$ ? cos ? ?

(Multiple Choice)

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Question 51

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. ) ?

(Multiple Choice)

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Question 52

Will Barrow wanted to know how tall the flagpole was in front of his school.To find its height,he drove a stake into the ground at the tip of the flagpole's shadow and recorded the angle of elevation at two different times during the day.He then measured the distance between the stakes.Will's data is below: Stake Time Angle of Elevation A 2:00 PM 82° B 3:00 PM 61° Distance between stakes A & B 10 feet Determine the height of the flagpole.Round your answer to nearest foot.

(Multiple Choice)

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Question 53

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\cos \theta = \frac { 1 } { 5 }$ ? sec ? and csc(90° - ?) ?

(Multiple Choice)

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Question 54

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ?sin 30° = $\frac { 1 } { 2 }$ ,cos 30° = $\frac { \sqrt { 3 } } { 2 }$ ? ?sin 60° and cos 60°

(Multiple Choice)

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Question 55

Evaluate each function.Round your answers to four decimal places. Tan15.7° and cot74.3°

(Multiple Choice)

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Question 56

Exam 25: Right Triangle Trigonometry

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ​ ​sin 90° = 1,tan 90° = Not defined Sin 0° and tan 0° ​

Construct an appropriate triangle to complete the table. (0∘≤θ≤90∘,0∘≤θ≤π2)\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)(0∘≤θ≤90∘,0∘≤θ≤2π​) Function \theta() \theta( rad ) Function Value ?

Using the figure below,if ? = 20° and y = 16,determine the exact value of r.

Evaluate each function.Round your answers to four decimal places.? cot⁡(π15)\cot \left( \frac { \pi } { 15 } \right)cot(15π​) and tan⁡π15\tan \frac { \pi } { 15 }tan15π​ ?

Using the figure below,if ? = 33° and y = 9,determine the exact value of x.

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity. ?

Find the exact value of csc ?,using the triangle shown in the figure below,if a=4a = 4a=4 and b=3b = 3b=3 .

Given sec⁡θ=10\sec \theta = \sqrt { 10 }secθ=10​ and tan ? = 3,determine the following. ? Cos(90° - ?) ?

Find the exact values of the six trigonometric functions of the angle ? for the triangle. ?

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? sec⁡θ=9\sec \theta = 9secθ=9 ? cos ? ?

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. ) ?

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? cos⁡θ=15\cos \theta = \frac { 1 } { 5 }cosθ=51​ ? sec ? and csc(90° - ?) ?

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ?sin 30° = 12\frac { 1 } { 2 }21​ ,cos 30° = 32\frac { \sqrt { 3 } } { 2 }23​​ ? ?sin 60° and cos 60°

Evaluate each function.Round your answers to four decimal places. ​ Tan15.7° and cot74.3° ​

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

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

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

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Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

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Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. sin 90° = 1,tan 90° = Not defined Sin 0° and tan 0°

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ Function \theta() \theta( rad ) Function Value ?

Evaluate each function.Round your answers to four decimal places.? $\cot \left( \frac { \pi } { 15 } \right)$ and $\tan \frac { \pi } { 15 }$ ?

Find the exact value of csc ?,using the triangle shown in the figure below,if $a = 4$ and $b = 3$ .

Given $\sec \theta = \sqrt { 10 }$ and tan ? = 3,determine the following. ? Cos(90° - ?) ?

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\sec \theta = 9$ ? cos ? ?

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\cos \theta = \frac { 1 } { 5 }$ ? sec ? and csc(90° - ?) ?

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ?sin 30° = $\frac { 1 } { 2 }$ ,cos 30° = $\frac { \sqrt { 3 } } { 2 }$ ? ?sin 60° and cos 60°

Evaluate each function.Round your answers to four decimal places. Tan15.7° and cot74.3°