Use the function value and constraint below to evaluate the given trigonometric function. $\begin{array} { c c c } \text { Function Value } & \text { Constraint } & \text { Evaluate: } \\ \sec \theta = - 5 & \tan \theta < 0 & \cot \theta \end{array}$

A) $- 2 \sqrt { 6 }$ B) $2 \sqrt { 6 }$ C) $- \frac { 1 } { 2 \sqrt { 6 } }$ D) $- \frac { 1 } { 5 }$ E) Undefined A) $- 2 \sqrt { 6 }$ B) $2 \sqrt { 6 }$ C) $- \frac { 1 } { 2 \sqrt { 6 } }$ D) $- \frac { 1 } { 5 }$ E) Undefined

Exam 4: Trigonometric Functions

A ship leaves port at noon and has a bearing of $\mathrm { S } 35 ^ { \circ } \mathrm { W }$ . The ship sails at 20 knots. How many nautical miles south will the ship have traveled by 8:00 P.M.? Round your answer to two decimals.

(Multiple Choice)

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Question 81

The terminal side of $\theta$ lies on the the line $12 x + 5 y = 0$ in the second quadrant. Find the exact value of $\tan \theta$ .

(Multiple Choice)

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Question 82

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = \frac { 11 \pi } { 6 }$ .

(Multiple Choice)

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Question 83

Find (if possible) the complement of $\frac { \pi } { 7 }$ .

(Multiple Choice)

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Question 84

Approximate $\tan ^ { - 1 } ( 3 )$ . Round your answer to four decimal places.

(Multiple Choice)

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Question 85

Convert the angle measure to decimal degree form $427 ^ { \circ } 50 ^ { \prime } 55 ^ { \prime \prime }$

(Multiple Choice)

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Question 86

Use a graphing utility to graph the function below, making sure to show at least two periods. $\sec \frac { x } { 2 }$

(Multiple Choice)

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Question 87

Evaluate the tangent of the angle without using a calculator. $- 300 ^ { \circ }$

(Multiple Choice)

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Question 88

Evaluate $\arccos \frac { \sqrt { 3 } } { 2 }$ without using a calculator.

(Multiple Choice)

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Question 89

Rewrite the given angle in radian measure as a multiple of $\pi$ . (Do not use a calculator.) $72 ^ { \circ }$

(Multiple Choice)

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Question 90

Find (if possible) the supplement of $\frac { 9 \pi } { 11 }$ .

(Multiple Choice)

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Question 91

Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$ . radius: $r = 12$ kilometers arc length: $s = 64$ kilometers

(Multiple Choice)

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Question 92

Determine two coterminal angles (one positive and one negative) for $\theta = \frac { 5 \pi } { 6 }$ .

(Multiple Choice)

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Question 93

Write an algebraic expression that is equivalent to $\sin \left( \arctan \frac { x } { 9 } \right)$ .

(Multiple Choice)

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Question 94

Determine a pair of coterminal angles (in radian measure) to the angle $\frac { \pi } { 3 }$ .

(Multiple Choice)

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Question 95

Use the function value and constraint below to evaluate the given trigonometric function. Function Value Constraint Evaluate: \theta=-5 \theta<0 \theta

(Multiple Choice)

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Question 96

A plane is 65 miles south and 60 miles west of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? Round your answer to the nearest degree.

(Multiple Choice)

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Question 97

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line. Line Quadrant Evaluate: y=10x I \theta

(Multiple Choice)

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Question 98

Find the indicated trigonometric value in the specified quadrant.

(Multiple Choice)

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Question 99

Use a calculator to evaluate $\tan 5.1$ . Round your answer to four decimal places.

(Multiple Choice)

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Question 100

A ship leaves port at noon and has a bearing of $\mathrm { S } 35 ^ { \circ } \mathrm { W }$ . The ship sails at 20 knots. How many nautical miles south will the ship have traveled by 8:00 P.M.? Round your answer to two decimals.

The terminal side of $\theta$ lies on the the line $12 x + 5 y = 0$ in the second quadrant. Find the exact value of $\tan \theta$ .

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = \frac { 11 \pi } { 6 }$ .

Find (if possible) the complement of $\frac { \pi } { 7 }$ .

Approximate $\tan ^ { - 1 } ( 3 )$ . Round your answer to four decimal places.

Convert the angle measure to decimal degree form $427 ^ { \circ } 50 ^ { \prime } 55 ^ { \prime \prime }$

Use a graphing utility to graph the function below, making sure to show at least two periods. $\sec \frac { x } { 2 }$

Evaluate the tangent of the angle without using a calculator. $- 300 ^ { \circ }$

Evaluate $\arccos \frac { \sqrt { 3 } } { 2 }$ without using a calculator.

Rewrite the given angle in radian measure as a multiple of $\pi$ . (Do not use a calculator.) $72 ^ { \circ }$

Find (if possible) the supplement of $\frac { 9 \pi } { 11 }$ .

Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$ . radius: $r = 12$ kilometers arc length: $s = 64$ kilometers

Determine two coterminal angles (one positive and one negative) for $\theta = \frac { 5 \pi } { 6 }$ .

Write an algebraic expression that is equivalent to $\sin \left( \arctan \frac { x } { 9 } \right)$ .

Determine a pair of coterminal angles (in radian measure) to the angle $\frac { \pi } { 3 }$ .

Use the function value and constraint below to evaluate the given trigonometric function. Function Value Constraint Evaluate: \theta=-5 \theta<0 \theta

A plane is 65 miles south and 60 miles west of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? Round your answer to the nearest degree.

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line. Line Quadrant Evaluate: y=10x I \theta

Find the indicated trigonometric value in the specified quadrant.

Use a calculator to evaluate $\tan 5.1$ . Round your answer to four decimal places.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Exam 4: Trigonometric Functions

A ship leaves port at noon and has a bearing of S35∘W\mathrm { S } 35 ^ { \circ } \mathrm { W }S35∘W . The ship sails at 20 knots. How many nautical miles south will the ship have traveled by 8:00 P.M.? Round your answer to two decimals.

The terminal side of θ\thetaθ lies on the the line 12x+5y=012 x + 5 y = 012x+5y=0 in the second quadrant. Find the exact value of tan⁡θ\tan \thetatanθ .

Find the point (x,y)( x , y )(x,y) on the unit circle corresponding to the real number t=11π6t = \frac { 11 \pi } { 6 }t=611π​ .

Find (if possible) the complement of π7\frac { \pi } { 7 }7π​ .

Approximate tan⁡−1(3)\tan ^ { - 1 } ( 3 )tan−1(3) . Round your answer to four decimal places.

Convert the angle measure to decimal degree form 427∘50′55′′427 ^ { \circ } 50 ^ { \prime } 55 ^ { \prime \prime }427∘50′55′′

Use a graphing utility to graph the function below, making sure to show at least two periods. sec⁡x2\sec \frac { x } { 2 }sec2x​

Evaluate the tangent of the angle without using a calculator. −300∘- 300 ^ { \circ }−300∘

Evaluate arccos⁡32\arccos \frac { \sqrt { 3 } } { 2 }arccos23​​ without using a calculator.

Rewrite the given angle in radian measure as a multiple of π\piπ . (Do not use a calculator.) 72∘72 ^ { \circ }72∘

Find (if possible) the supplement of 9π11\frac { 9 \pi } { 11 }119π​ .

Find the radian measure of the central angle of a circle of radius rrr that intercepts an arc of length sss . radius: r=12r = 12r=12 kilometers arc length: s=64s = 64s=64 kilometers

Determine two coterminal angles (one positive and one negative) for θ=5π6\theta = \frac { 5 \pi } { 6 }θ=65π​ .

Write an algebraic expression that is equivalent to sin⁡(arctan⁡x9)\sin \left( \arctan \frac { x } { 9 } \right)sin(arctan9x​) .

Determine a pair of coterminal angles (in radian measure) to the angle π3\frac { \pi } { 3 }3π​ .

Use the function value and constraint below to evaluate the given trigonometric function. Function Value Constraint Evaluate: \theta=-5 \theta<0 \theta

A plane is 65 miles south and 60 miles west of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? Round your answer to the nearest degree.

The terminal side of θ\thetaθ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of θ\thetaθ by finding a point on the line. Line Quadrant Evaluate: y=10x I \theta

Find the indicated trigonometric value in the specified quadrant.

Use a calculator to evaluate tan⁡5.1\tan 5.1tan5.1 . Round your answer to four decimal places.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

A ship leaves port at noon and has a bearing of $\mathrm { S } 35 ^ { \circ } \mathrm { W }$ . The ship sails at 20 knots. How many nautical miles south will the ship have traveled by 8:00 P.M.? Round your answer to two decimals.

The terminal side of $\theta$ lies on the the line $12 x + 5 y = 0$ in the second quadrant. Find the exact value of $\tan \theta$ .

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = \frac { 11 \pi } { 6 }$ .

Find (if possible) the complement of $\frac { \pi } { 7 }$ .

Approximate $\tan ^ { - 1 } ( 3 )$ . Round your answer to four decimal places.

Convert the angle measure to decimal degree form $427 ^ { \circ } 50 ^ { \prime } 55 ^ { \prime \prime }$

Use a graphing utility to graph the function below, making sure to show at least two periods. $\sec \frac { x } { 2 }$

Evaluate the tangent of the angle without using a calculator. $- 300 ^ { \circ }$

Evaluate $\arccos \frac { \sqrt { 3 } } { 2 }$ without using a calculator.

Rewrite the given angle in radian measure as a multiple of $\pi$ . (Do not use a calculator.) $72 ^ { \circ }$

Find (if possible) the supplement of $\frac { 9 \pi } { 11 }$ .

Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$ . radius: $r = 12$ kilometers arc length: $s = 64$ kilometers

Determine two coterminal angles (one positive and one negative) for $\theta = \frac { 5 \pi } { 6 }$ .

Write an algebraic expression that is equivalent to $\sin \left( \arctan \frac { x } { 9 } \right)$ .

Determine a pair of coterminal angles (in radian measure) to the angle $\frac { \pi } { 3 }$ .

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line. Line Quadrant Evaluate: y=10x I \theta

Use a calculator to evaluate $\tan 5.1$ . Round your answer to four decimal places.