Stewart Precalc 6e Chapter 5 Test: Trigonometric Functions of Real Numbers

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Stewart Precalc 6e Chapter 5 Test: Trigonometric Functions of Real Numbers 0/28
1 Chapter Test - Unit Circle · Level 2
The point \(P(x, y)\) is on the unit circle in Quadrant
IV. If \(x = \dfrac{\sqrt{11}}{6}\), find \(y\).
2 Chapter Test - Trigonometric Functions · Level 2
The point \(P\) in the figure has \(y\)-coordinate \(\dfrac{4}{5}\). Find:
question image
(a) \(\sin t\)
(b) \(\cos t\)
(c) \(\tan t\)
(d) \(\sec t\)

Enter your answer directly below each part above.

3 Chapter Test - Special Trig Values · Level 3
Find the exact value.
(a) \(\sin \dfrac{7 \pi}{6}\)
(b) \(\cos \dfrac{13 \pi}{4}\)
(c) \(\tan\left(-\dfrac{5 \pi}{3}\right)\)
(d) \(\csc \dfrac{3 \pi}{2}\)

Enter your answer directly below each part above.

4 Chapter Test - Trigonometric Identities · Level 3
Express \(\tan t\) in terms of \(\sin t\), if the terminal point determined by \(t\) is in Quadrant II.
5 Chapter Test - Evaluating Trig Expressions · Level 3
If \(\cos t = -\dfrac{8}{17}\) and if the terminal point determined by \(t\) is in Quadrant III, find \(\tan t \cot t + \csc t\).
6 Chapter Test - Graphing Trigonometric Functions · Level 2
A trigonometric function is given.
(a) Find the amplitude, period, and phase shift of the function.
(b) Sketch the graph. \(y = -5 \cos 4 x\)

Enter your answer directly below each part above.

7 Chapter Test - Graphing Trigonometric Functions · Level 3
A trigonometric function is given.
(a) Find the amplitude, period, and phase shift of the function.
(b) Sketch the graph. \(y = 2 \sin\left(\dfrac{1}{2} x - \dfrac{\pi}{6}\right)\)

Enter your answer directly below each part above.

8 Chapter Test - Period of Trigonometric Functions · Level 3
Find the period, and graph the function. \(y = -\csc 2 x\)
9 Chapter Test - Period of Trigonometric Functions · Level 3
Find the period, and graph the function. \(y = \tan\left(2 x - \dfrac{\pi}{2}\right)\)
10 Chapter Test - Inverse Trigonometric Functions · Level 3
Find the exact value of each expression, if it is defined.
(a) \(\tan^{-1} 1\)
(b) \(\cos^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\)
(c) \(\tan^{-1}(\tan 3 \pi)\)
(d) \(\cos(\tan^{-1}(-\sqrt{3}))\)

Enter your answer directly below each part above.

11 Chapter Test - Modeling from Graphs · Level 4
The graph shown is one period of a function of the form \(y = a \sin k(x - b)\). Determine the function.
question image
12 Chapter Test - Graph Analysis · Level 3
Let \(f(x) = \dfrac{\cos x}{1 + x^2}\).
(a) Use a graphing device to graph \(f\) in an appropriate viewing rectangle.
(b) Determine from the graph if \(f\) is even, odd, or neither.
(c) Find the minimum and maximum values of \(f\).

Enter your answer directly below each part above.

13 Chapter Test - Simple Harmonic Motion · Level 3
A mass suspended from a spring oscillates in simple harmonic motion. The mass completes 2 cycles every second, and the distance between the highest point and the lowest point of the oscillation is 10 cm. Find an equation of the form \(y = a \sin \omega t\) that gives the distance of the mass from its rest position as a function of time.
14 Chapter Test - Damped Harmonic Motion · Level 4
An object is moving up and down in damped harmonic motion. Its displacement at time \(t = 0\) is 16 in.; this is its maximum displacement. The damping constant is \(c = 0.1\), and the frequency is 12 Hz.
question image
(a) Find a function that models this motion.
(b) Graph the function.

Enter your answer directly below each part above.

15 Unit Circle · Level 2
The point \(P(x, y)\) is on the unit circle in Quadrant
IV. If \(x = \dfrac{\sqrt{11}}{6}\), find \(y\).
16 Unit Circle - Trigonometric Functions · Level 3
The point \(P\) in the figure at the left has \(y\)-coordinate \(\dfrac{4}{5}\). Find:
question image
(a) \(\sin t\)
(b) \(\cos t\)
(c) \(\tan t\)
(d) \(\sec t\)

Enter your answer directly below each part above.

17 Exact Trigonometric Values · Level 3
Find the exact value.
(a) \(\sin \dfrac{7 \pi}{6}\)
(b) \(\cos \dfrac{13 \pi}{4}\)
(c) \(\tan\left(-\dfrac{5 \pi}{3}\right)\)
(d) \(\csc \dfrac{3 \pi}{2}\)

Enter your answer directly below each part above.

18 Fundamental Identities · Level 3
Express \(\tan t\) in terms of \(\sin t\), if the terminal point determined by \(t\) is in Quadrant II.
19 Trigonometric Expressions · Level 3
If \(\cos t = -\dfrac{8}{17}\) and if the terminal point determined by \(t\) is in Quadrant III, find \(\tan t \cot t + \csc t\).
20 Amplitude, Period, Phase Shift · Level 3
A trigonometric function is given.
(a) Find the amplitude, period, and phase shift of the function.
(b) Sketch the graph. \(y = -5 \cos(4 x)\)

Enter your answer directly below each part above.

21 Amplitude, Period, Phase Shift · Level 3
A trigonometric function is given.
(a) Find the amplitude, period, and phase shift of the function.
(b) Sketch the graph. \(y = 2 \sin\left(\dfrac{1}{2} x - \dfrac{\pi}{6}\right)\)

Enter your answer directly below each part above.

22 Period and Graph - Cosecant · Level 3
Find the period, and graph the function. \(y = -\csc(2 x)\)
23 Period and Graph - Tangent · Level 3
Find the period, and graph the function. \(y = \tan\left(2 x - \dfrac{\pi}{2}\right)\)
24 Inverse Trigonometric Functions · Level 3
Find the exact value of each expression, if it is defined.
(a) \(\tan^{-1}(1)\)
(b) \(\cos^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\)
(c) \(\tan^{-1}(\tan 3 \pi)\)
(d) \(\cos(\tan^{-1}(-\sqrt{3}))\)

Enter your answer directly below each part above.

25 Determining Function from Graph · Level 4
The graph shown at left is one period of a function of the form \(y = a \sin(k(x - b))\). Determine the function.
26 Function Analysis · Level 4
Let \(f(x) = \dfrac{\cos x}{1 + x^2}\).
(a) Use a graphing device to graph \(f\) in an appropriate viewing rectangle.
(b) Determine from the graph if \(f\) is even, odd, or neither.
(c) Find the minimum and maximum values of \(f\).

Enter your answer directly below each part above.

27 Simple Harmonic Motion · Level 4
A mass suspended from a spring oscillates in simple harmonic motion. The mass completes 2 cycles every second, and the distance between the highest point and the lowest point of the oscillation is 10 cm. Find an equation of the form \(y = a \sin(\omega t)\) that gives the distance of the mass from its rest position as a function of time.
28 Damped Harmonic Motion · Level 4
An object is moving up and down in damped harmonic motion. Its displacement at time \(t = 0\) is 16 in; this is its maximum displacement. The damping constant is \(c = 0.1\), and the frequency is 12 Hz.
(a) Find a function that models this motion.
(b) Graph the function.

Enter your answer directly below each part above.

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