Exam 4: Trigonometric Functions

Match the function with its graph. -1) $y = \tan x$ 2) $y = \cot x$ 3) $y = - \tan x$ 4) $y = - \cot x$ a. $Match the function with its graph. -1) y = \tan x 2) y = \cot x 3) y = - \tan x 4) y = - \cot x a. b. c. d.$ b. $Match the function with its graph. -1) y = \tan x 2) y = \cot x 3) y = - \tan x 4) y = - \cot x a. b. c. d.$ c. $Match the function with its graph. -1) y = \tan x 2) y = \cot x 3) y = - \tan x 4) y = - \cot x a. b. c. d.$ d. $Match the function with its graph. -1) y = \tan x 2) y = \cot x 3) y = - \tan x 4) y = - \cot x a. b. c. d.$

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Question 401

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - $Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find \cos B and \cot B .$ Find $\cos B$ and $\cot B$ .

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Question 402

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = \left| \cos \frac { 1 } { 4 } x \right|$

(Multiple Choice)

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Question 403

Evaluate without using a calculator by using ratios in a reference triangle. - $\csc 330 ^ { \circ }$

(Multiple Choice)

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Question 404

Solve the problem. -The temperature in Fairbanks is approximated by $T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25$ where $T ( x )$ is the temperature on day $x$ , with $x = 1$ corresponding to Jan. 1 and $x = 365$ corresponding to Dec. 31 . Estimate the temperature on day 300 .

(Multiple Choice)

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Question 405

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\tan x = 5 \sin x$

(Multiple Choice)

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Question 406

Find the exact value of the composition. - $\cos \left( \frac { 1 } { 2 } \arcsin \left( \frac { 5 } { 13 } \right) \right)$

(Multiple Choice)

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Question 407

Find the exact value of the real number y. - $y = \sin ^ { - 1 } ( 1 )$

(Multiple Choice)

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Question 408

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

(Multiple Choice)

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Question 409

Find the domain and range of the function. - $f ( x ) = - 4 \cos ^ { 2 } x$

(Multiple Choice)

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Question 410

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $- 87 ^ { \circ }$

(Multiple Choice)

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Question 411

Solve the problem. -Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be $22 ^ { \circ } 53 ^ { \prime }$ . He then drives 1 mile $( 1$ mile $= 5280 \mathrm { ft } )$ more and measures the angle of elevation to be $32 ^ { \circ } 7 ^ { \prime }$ . Find the height of the mountain to the nearest foot.

(Multiple Choice)

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Question 412

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ and $\tan \theta < 0$

(Multiple Choice)

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Question 413

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant I, sect

(Multiple Choice)

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Question 414

Evaluate without using a calculator. - $\tan \alpha$ , if $\sec \alpha = \frac { 9 } { 4 }$ and $\csc \theta < 0$

(Multiple Choice)

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Question 415

Determine the sign (positive or negative) of the given value without use of a calculator. - $\sin \frac { 4 \pi } { 3 }$

(Multiple Choice)

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Question 416

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $\frac { 5 \pi } { 9 }$

(Multiple Choice)

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Question 417

Solve the right triangle for all missing sides and angles to the nearest tenth. -

(Multiple Choice)

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Question 418

Find the exact value of the composition. - $\cos \left( \arcsin \left( \frac { 1 } { 4 } \right) \right)$

(Multiple Choice)

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Question 419

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = \frac { 1 } { 5 } \sin \frac { 3 x } { 5 } ; g ( x ) = \sin x$

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Question 420

Showing 401 - 420 of 522

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - $Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find \cos B and \cot B .$ Find $\cos B$ and $\cot B$ .

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = \left| \cos \frac { 1 } { 4 } x \right|$

Evaluate without using a calculator by using ratios in a reference triangle. - $\csc 330 ^ { \circ }$

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\tan x = 5 \sin x$

Find the exact value of the composition. - $\cos \left( \frac { 1 } { 2 } \arcsin \left( \frac { 5 } { 13 } \right) \right)$

Find the exact value of the real number y. - $y = \sin ^ { - 1 } ( 1 )$

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

Find the domain and range of the function. - $f ( x ) = - 4 \cos ^ { 2 } x$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $- 87 ^ { \circ }$

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ and $\tan \theta < 0$

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant I, sect

Evaluate without using a calculator. - $\tan \alpha$ , if $\sec \alpha = \frac { 9 } { 4 }$ and $\csc \theta < 0$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\sin \frac { 4 \pi } { 3 }$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $\frac { 5 \pi } { 9 }$

Solve the right triangle for all missing sides and angles to the nearest tenth. -

Find the exact value of the composition. - $\cos \left( \arcsin \left( \frac { 1 } { 4 } \right) \right)$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = \frac { 1 } { 5 } \sin \frac { 3 x } { 5 } ; g ( x ) = \sin x$

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

Match the function with its graph. -1) y=tan⁡xy = \tan xy=tanx 2) y=cot⁡xy = \cot xy=cotx 3) y=−tan⁡xy = - \tan xy=−tanx 4) y=−cot⁡xy = - \cot xy=−cotx a. b. c. d.

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find cos⁡B\cos BcosB and cot⁡B\cot BcotB .

Determine whether the function is periodic. If it is periodic, find the period. - f(x)=∣cos⁡14x∣f ( x ) = \left| \cos \frac { 1 } { 4 } x \right|f(x)=​cos41​x​

Evaluate without using a calculator by using ratios in a reference triangle. - csc⁡330∘\csc 330 ^ { \circ }csc330∘

Find approximate solutions for the equation in the interval −π<X<π -\pi<\mathbf{X}<\pi −π<X<π . Round to three decimal places. - tan⁡x=5sin⁡x\tan x = 5 \sin xtanx=5sinx

Find the exact value of the composition. - cos⁡(12arcsin⁡(513))\cos \left( \frac { 1 } { 2 } \arcsin \left( \frac { 5 } { 13 } \right) \right)cos(21​arcsin(135​))

Find the exact value of the real number y. - y=sin⁡−1(1)y = \sin ^ { - 1 } ( 1 )y=sin−1(1)

Find an algebraic expression equivalent to the given expression. - sin⁡(arcsec⁡u)\sin ( \operatorname { arcsec } u )sin(arcsecu)

Find the domain and range of the function. - f(x)=−4cos⁡2xf ( x ) = - 4 \cos ^ { 2 } xf(x)=−4cos2x

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - −87∘- 87 ^ { \circ }−87∘

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - sin⁡θ=32\sin \theta = \frac { \sqrt { 3 } } { 2 }sinθ=23​​ and tan⁡θ<0\tan \theta < 0tanθ<0

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant I, sect

Evaluate without using a calculator. - tan⁡α\tan \alphatanα , if sec⁡α=94\sec \alpha = \frac { 9 } { 4 }secα=49​ and csc⁡θ<0\csc \theta < 0cscθ<0

Determine the sign (positive or negative) of the given value without use of a calculator. - sin⁡4π3\sin \frac { 4 \pi } { 3 }sin34π​

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - 5π9\frac { 5 \pi } { 9 }95π​

Solve the right triangle for all missing sides and angles to the nearest tenth. -

Find the exact value of the composition. - cos⁡(arcsin⁡(14))\cos \left( \arcsin \left( \frac { 1 } { 4 } \right) \right)cos(arcsin(41​))

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - f(x)=15sin⁡3x5;g(x)=sin⁡xf ( x ) = \frac { 1 } { 5 } \sin \frac { 3 x } { 5 } ; g ( x ) = \sin xf(x)=51​sin53x​;g(x)=sinx

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

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - $Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find \cos B and \cot B .$ Find $\cos B$ and $\cot B$ .

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = \left| \cos \frac { 1 } { 4 } x \right|$

Evaluate without using a calculator by using ratios in a reference triangle. - $\csc 330 ^ { \circ }$

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\tan x = 5 \sin x$

Find the exact value of the composition. - $\cos \left( \frac { 1 } { 2 } \arcsin \left( \frac { 5 } { 13 } \right) \right)$

Find the exact value of the real number y. - $y = \sin ^ { - 1 } ( 1 )$

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

Find the domain and range of the function. - $f ( x ) = - 4 \cos ^ { 2 } x$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $- 87 ^ { \circ }$

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ and $\tan \theta < 0$

Evaluate without using a calculator. - $\tan \alpha$ , if $\sec \alpha = \frac { 9 } { 4 }$ and $\csc \theta < 0$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\sin \frac { 4 \pi } { 3 }$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $\frac { 5 \pi } { 9 }$

Find the exact value of the composition. - $\cos \left( \arcsin \left( \frac { 1 } { 4 } \right) \right)$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = \frac { 1 } { 5 } \sin \frac { 3 x } { 5 } ; g ( x ) = \sin x$