Exam 4: Trigonometric Functions

Solve. -A formula for the up-and-down motion of a weight on a spring is given by $S = 2 \sin \left( \frac { \sqrt { k } } { m } \right) t$ , where $k$ is the spring constant, $\mathrm { m }$ is the mass, and $t$ is the time. Solve the equation for $\mathrm { t }$ .

(Multiple Choice)

4.8/5

(75)

Question 141

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $210 ^ { \circ }$

(Multiple Choice)

4.9/5

(95)

Question 142

Solve the problem. -The minute hand of a clock is 15 inches long. What distance does its tip move in 27 minutes?

(Multiple Choice)

4.8/5

(90)

Question 143

Graph the function. - $y=\sin \pi x$ $Graph the function. - y=\sin \pi x$

(Multiple Choice)

4.9/5

(66)

Question 144

Find the domain and range of the function. - $f ( x ) = 5 | x | + \sin x$

(Multiple Choice)

4.8/5

(82)

Question 145

Choose the point on the terminal side of . - $\theta = - 210 ^ { \circ }$

(Multiple Choice)

4.9/5

(89)

Question 146

Graph the function. - $y=-4 \cot x$ $Graph the function. - y=-4 \cot x$

(Multiple Choice)

4.7/5

(86)

Question 147

Use a calculator to solve for x in the given interval - $\csc \theta = 5.731,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

(Multiple Choice)

4.9/5

(66)

Question 148

Solve the problem. -A rocket is fired at an angle of $21 ^ { \circ }$ with the ground. Find the distance traveled by the rocket when it has reached an altitude of 175 feet. Give your answer to the nearest foot.

(Multiple Choice)

4.8/5

(83)

Question 149

Find an algebraic expression equivalent to the given expression. - $\cos ( \operatorname { arccot } u )$

(Multiple Choice)

4.7/5

(92)

Question 150

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\sec \theta = \frac { 5 } { 4 } ; \sin \theta$

(Multiple Choice)

4.7/5

(95)

Question 151

Evaluate without using a calculator by using ratios in a reference triangle. - $\tan 300 ^ { \circ }$

(Multiple Choice)

4.7/5

(69)

Question 152

Solve the equation. -Solve $\cot \theta = \sqrt { 3 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

(Multiple Choice)

4.8/5

(90)

Question 153

Solve the problem. -Determine the period and frequency of oscillation when a pendulum of length 7 feet is released after being displaced 2 radians.

(Multiple Choice)

4.7/5

(71)

Question 154

Find the amplitude of the function. - $y = - 3 \sin x$

(Multiple Choice)

4.9/5

(79)

Question 155

Solve the problem. -City $X$ is 50 miles due south of City $Y$ , and City $Z$ is 25 miles due west of City X. What is the bearing of City Z from City $Y$ (to the nearest tenth of a degree)?

(Multiple Choice)

4.8/5

(82)

Question 156

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\cos \left( \frac { \pi } { 9 } \right)$

(Multiple Choice)

4.7/5

(83)

Question 157

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\cos ^ { - 1 } ( - 0.9397 )$

(Multiple Choice)

4.8/5

(91)

Question 158

Determine the sign (positive or negative) of the given value without use of a calculator. - $\cos \left( - \frac { \pi } { 8 } \right)$

(Multiple Choice)

4.7/5

(76)

Question 159

Evaluate. - $\tan \left( \frac { \pi } { 6 } + 2716 \pi \right)$

(Multiple Choice)

4.8/5

(79)

Question 160

Solve. -A formula for the up-and-down motion of a weight on a spring is given by $S = 2 \sin \left( \frac { \sqrt { k } } { m } \right) t$ , where $k$ is the spring constant, $\mathrm { m }$ is the mass, and $t$ is the time. Solve the equation for $\mathrm { t }$ .

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $210 ^ { \circ }$

Solve the problem. -The minute hand of a clock is 15 inches long. What distance does its tip move in 27 minutes?

Graph the function. - $y=\sin \pi x$ $Graph the function. - y=\sin \pi x$

Find the domain and range of the function. - $f ( x ) = 5 | x | + \sin x$

Choose the point on the terminal side of . - $\theta = - 210 ^ { \circ }$

Graph the function. - $y=-4 \cot x$ $Graph the function. - y=-4 \cot x$

Use a calculator to solve for x in the given interval - $\csc \theta = 5.731,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Solve the problem. -A rocket is fired at an angle of $21 ^ { \circ }$ with the ground. Find the distance traveled by the rocket when it has reached an altitude of 175 feet. Give your answer to the nearest foot.

Find an algebraic expression equivalent to the given expression. - $\cos ( \operatorname { arccot } u )$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\sec \theta = \frac { 5 } { 4 } ; \sin \theta$

Evaluate without using a calculator by using ratios in a reference triangle. - $\tan 300 ^ { \circ }$

Solve the equation. -Solve $\cot \theta = \sqrt { 3 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Solve the problem. -Determine the period and frequency of oscillation when a pendulum of length 7 feet is released after being displaced 2 radians.

Find the amplitude of the function. - $y = - 3 \sin x$

Solve the problem. -City $X$ is 50 miles due south of City $Y$ , and City $Z$ is 25 miles due west of City X. What is the bearing of City Z from City $Y$ (to the nearest tenth of a degree)?

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\cos \left( \frac { \pi } { 9 } \right)$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\cos ^ { - 1 } ( - 0.9397 )$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\cos \left( - \frac { \pi } { 8 } \right)$

Evaluate. - $\tan \left( \frac { \pi } { 6 } + 2716 \pi \right)$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 4: Trigonometric Functions

Solve. -A formula for the up-and-down motion of a weight on a spring is given by S=2sin⁡(km)tS = 2 \sin \left( \frac { \sqrt { k } } { m } \right) tS=2sin(mk​​)t , where kkk is the spring constant, m\mathrm { m }m is the mass, and ttt is the time. Solve the equation for t\mathrm { t }t .

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 210∘210 ^ { \circ }210∘

Solve the problem. -The minute hand of a clock is 15 inches long. What distance does its tip move in 27 minutes?

Graph the function. - y=sin⁡πxy=\sin \pi xy=sinπx

Find the domain and range of the function. - f(x)=5∣x∣+sin⁡xf ( x ) = 5 | x | + \sin xf(x)=5∣x∣+sinx

Choose the point on the terminal side of . - θ=−210∘\theta = - 210 ^ { \circ }θ=−210∘

Graph the function. - y=−4cot⁡xy=-4 \cot xy=−4cotx

Use a calculator to solve for x in the given interval - csc⁡θ=5.731,0∘≤θ≤90∘\csc \theta = 5.731,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }cscθ=5.731,0∘≤θ≤90∘

Solve the problem. -A rocket is fired at an angle of 21∘21 ^ { \circ }21∘ with the ground. Find the distance traveled by the rocket when it has reached an altitude of 175 feet. Give your answer to the nearest foot.

Find an algebraic expression equivalent to the given expression. - cos⁡(arccot⁡u)\cos ( \operatorname { arccot } u )cos(arccotu)

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - sec⁡θ=54;sin⁡θ\sec \theta = \frac { 5 } { 4 } ; \sin \thetasecθ=45​;sinθ

Evaluate without using a calculator by using ratios in a reference triangle. - tan⁡300∘\tan 300 ^ { \circ }tan300∘

Solve the equation. -Solve cot⁡θ=3\cot \theta = \sqrt { 3 }cotθ=3​ for θ\thetaθ , where 0∘≤θ≤90∘0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }0∘≤θ≤90∘

Solve the problem. -Determine the period and frequency of oscillation when a pendulum of length 7 feet is released after being displaced 2 radians.

Find the amplitude of the function. - y=−3sin⁡xy = - 3 \sin xy=−3sinx

Solve the problem. -City XXX is 50 miles due south of City YYY , and City ZZZ is 25 miles due west of City X. What is the bearing of City Z from City YYY (to the nearest tenth of a degree)?

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - cos⁡(π9)\cos \left( \frac { \pi } { 9 } \right)cos(9π​)

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - cos⁡−1(−0.9397)\cos ^ { - 1 } ( - 0.9397 )cos−1(−0.9397)

Determine the sign (positive or negative) of the given value without use of a calculator. - cos⁡(−π8)\cos \left( - \frac { \pi } { 8 } \right)cos(−8π​)

Evaluate. - tan⁡(π6+2716π)\tan \left( \frac { \pi } { 6 } + 2716 \pi \right)tan(6π​+2716π)

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Solve. -A formula for the up-and-down motion of a weight on a spring is given by $S = 2 \sin \left( \frac { \sqrt { k } } { m } \right) t$ , where $k$ is the spring constant, $\mathrm { m }$ is the mass, and $t$ is the time. Solve the equation for $\mathrm { t }$ .

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $210 ^ { \circ }$

Graph the function. - $y=\sin \pi x$ $Graph the function. - y=\sin \pi x$

Find the domain and range of the function. - $f ( x ) = 5 | x | + \sin x$

Choose the point on the terminal side of . - $\theta = - 210 ^ { \circ }$

Graph the function. - $y=-4 \cot x$ $Graph the function. - y=-4 \cot x$

Use a calculator to solve for x in the given interval - $\csc \theta = 5.731,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Solve the problem. -A rocket is fired at an angle of $21 ^ { \circ }$ with the ground. Find the distance traveled by the rocket when it has reached an altitude of 175 feet. Give your answer to the nearest foot.

Find an algebraic expression equivalent to the given expression. - $\cos ( \operatorname { arccot } u )$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\sec \theta = \frac { 5 } { 4 } ; \sin \theta$

Evaluate without using a calculator by using ratios in a reference triangle. - $\tan 300 ^ { \circ }$

Solve the equation. -Solve $\cot \theta = \sqrt { 3 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Find the amplitude of the function. - $y = - 3 \sin x$

Solve the problem. -City $X$ is 50 miles due south of City $Y$ , and City $Z$ is 25 miles due west of City X. What is the bearing of City Z from City $Y$ (to the nearest tenth of a degree)?

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\cos \left( \frac { \pi } { 9 } \right)$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\cos ^ { - 1 } ( - 0.9397 )$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\cos \left( - \frac { \pi } { 8 } \right)$

Evaluate. - $\tan \left( \frac { \pi } { 6 } + 2716 \pi \right)$