Multiple ChoiceSketch the function y=cos(x)−1y=\cos\left(x\right)-1y=cos(x)−1 on the graph below.179views1rank
Multiple ChoiceDetermine the value of y=sin(−π2)+50y=\sin\left(-\frac{\pi}{2}\right)+50y=sin(−2π)+50 without using a calculator or the unit circle.165views3rank
Multiple ChoiceDetermine the value of y=−2⋅sin(−3π2)+10y=-2\cdot\sin\left(-\frac{3\pi}{2}\right)+10y=−2⋅sin(−23π)+10 without using a calculator or the unit circle.155views2rank
Multiple ChoiceGiven below is the graph of the function y=sin(bx)y=\sin\left(bx\right)y=sin(bx). Determine the correct value for b.211views
Multiple ChoiceThe Period for the function y=cos(bx)y=\cos\left(bx\right)y=cos(bx) is T=20πT=20\piT=20π. Determine the correct value of b.166views4rank
Textbook QuestionIn Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 4 sin x336views
Textbook QuestionIn Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 1/3 sin x244views
Textbook QuestionAn object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.𝒮(t) = 5 cos 2tWhat is the amplitude of this motion?171views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = sin (x + π/4) is obtained by shifting the graph of y = sin x ______ unit(s) to the ________ (right/left).155views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 3 - ¼ cos ⅔ x161views
Textbook QuestionMatch each function with its graph in choices A–I. (One choice will not be used.)y = cos (x - π/4)A. <IMAGE> B. <IMAGE> C. <IMAGE>D. <IMAGE> E. <IMAGE> F. <IMAGE>G. <IMAGE> H. <IMAGE> I. <IMAGE>166views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 3 cos (x + π/2)170views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = -sin (x - 3π/4)156views
Textbook QuestionGraph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.y = 2 cos x235views
Textbook QuestionGraph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.y = ⅔ sin x420views1comments
Textbook QuestionMatch each function with its graph in choices A–I. (One choice will not be used.) y = -1 + cos xA. <IMAGE> B. <IMAGE> C. <IMAGE>D. <IMAGE> E. <IMAGE> F. <IMAGE>G. <IMAGE> H. <IMAGE> I. <IMAGE>249views
Textbook QuestionGraph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.y = -2 sin x234views
Textbook QuestionMatch each function in Column I with the appropriate description in Column II. I y = 3 sin(2x - 4) IIA. amplitude = 2, period = π/2, phase shift = ¾B. amplitude = 3, period = π, phase shift = 2C. amplitude = 4, period = 2π/3, phase shift = ⅔D. amplitude = 2, period = 2π/3, phase shift = 4⁄3177views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = cos (x - π/6) is obtained by shifting the graph of y = cos x ______ unit(s) to the ________ (right/left).185views
Textbook QuestionAn object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.𝒮(t) = 5 cos 2tWhat is the period of this motion?165views
Textbook QuestionMatch each function in Column I with the appropriate description in Column II.Iy = -4 sin(3x - 2)IIA. amplitude = 2, period = π/2, phase shift = ¾B. amplitude = 3, period = π, phase shift = 2C. amplitude = 4, period = 2π/3, phase shift = ⅔D. amplitude = 2, period = 2π/3, phase shift = 4⁄3172views
Textbook QuestionGraph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.y = sin ⅔ x184views
Textbook QuestionGraph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.y = sin 3x177views
Textbook QuestionEach function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.<IMAGE>178views
Textbook QuestionEach function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.<IMAGE>276views
Textbook QuestionGraph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.y = 2 sin ¼ x354views
Textbook QuestionEach function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.<IMAGE>176views
Textbook QuestionAn object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.𝒮(t) = 5 cos 2tWhat is the frequency?184views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of ________.173views
Textbook QuestionGraph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.y = -2 cos 3x197views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 2 sin (x + π)172views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = -¼ cos (½ x + π/2)175views
Textbook QuestionDecide whether each statement is true or false. If false, explain why.The graph of y = sec x in Figure 37 suggests that sec(-x) = sec x for all x in the domain of sec x.165views
Textbook QuestionGraph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.y = -2 sin 2 πx236views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 3 cos [π/2 (x - ½)]172views
Textbook QuestionGraph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.y = ½ cos π x 2286views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 2 - sin(3x - π/5)223views
Textbook QuestionGraph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.y = π sin πx207views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = -3 sin x is obtained by stretching the graph of y = sin x by a factor of ________ and reflecting across the ________-axis.192views
Textbook QuestionDetermine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.<IMAGE>173views
Textbook QuestionDetermine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.<IMAGE>348views
Textbook QuestionDetermine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.<IMAGE>230views
Textbook QuestionDetermine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts.<IMAGE>174views
Textbook QuestionDetermine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.<IMAGE>194views
Textbook QuestionDetermine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts.<IMAGE>177views
Textbook QuestionDetermine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.<IMAGE>239views
Textbook QuestionGraph each function over a one-period interval. See Example 3.y = (3/2) sin [2(x + π/4)]181views
Textbook QuestionDetermine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.<IMAGE>212views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 2 sin 2x166views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = 6 + 3 sin x is obtained by shifting the graph of y = 3 sin x ________ unit(s) __________ (up/down).174views
Textbook QuestionGraph each function over a two-period interval. See Example 4.y = -3 + 2 sin x159views
Textbook QuestionGraph each function over a two-period interval. See Example 4.y = -1 - 2 cos 5x176views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = -5 + 2 cos x is obtained by shifting the graph of y = 2 cos x ________ unit(s) __________ (up/down).158views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = -½ cos 3x192views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = 3 + 5 cos (x + π/5) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)193views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 2 sin 5x189views
Textbook QuestionFill in the blank(s) to correctly complete each sentence.The graph of y = -2 + 3 cos (x - π/6) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)158views
Textbook QuestionMatch each function with its graph in choices A–I. (One choice will not be used.)y = sin (x - π/4)A. <IMAGE> B. <IMAGE> C. <IMAGE>D. <IMAGE> E. <IMAGE> F. <IMAGE>G. <IMAGE> H. <IMAGE> I. <IMAGE>194views
Textbook QuestionFor each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 1 + 2 sin ¼ x173views
Textbook QuestionIn Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = -3 sin x473views
Textbook QuestionIn Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin 1/2 x306views
Textbook QuestionIn Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = -3 sin 2πx324views
Textbook QuestionIn Exercises 12–13, use a vertical shift to graph one period of the function. y = 2 cos 1/3 x − 2259views
Textbook QuestionIn Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = -sin 2/3 x267views
Textbook QuestionIn Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = sin x + cos 1/2 x203views
Textbook QuestionIn Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = sin(x − π)340views
Textbook QuestionIn Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 3 sin(2x − π)343views
Textbook QuestionIn Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 1/2 sin(x + π/2)252views
Textbook QuestionIn Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −2 sin(2x + π/2)578views
Textbook QuestionConcept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (a) x-axis (5, -3)172views
Textbook QuestionConcept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (b) y-axis (5, -3)166views
Textbook QuestionConcept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (c) origin. (5, -3)147views
Textbook QuestionConcept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (a) x-axis (-4, -2)157views
Textbook QuestionConcept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (b) y-axis. (-4, -2)144views
Textbook QuestionConcept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (c) origin. (-4, -2)144views
Textbook QuestionDetermine whether each function is even, odd, or neither. See Example 5. ƒ(x) = -x³ + 2x171views
Textbook QuestionDetermine whether each function is even, odd, or neither. See Example 5. ƒ(x) = 0.5x⁴ - 2x² + 6147views
Textbook QuestionIn Exercises 53–60, use a vertical shift to graph one period of the function. y = sin x + 2220views
Textbook QuestionDetermine whether each function is even, odd, or neither. See Example 5. ƒ(x) = x³ - x + 9313views
Textbook QuestionDetermine whether each function is even, odd, or neither. See Example 5. 1 ƒ(x) = x + —— x⁵136views
Textbook QuestionIn Exercises 53–60, use a vertical shift to graph one period of the function. y = cos x + 3210views
Textbook QuestionIn Exercises 53–60, use a vertical shift to graph one period of the function. y = −3 sin 2πx + 2244views
Textbook QuestionIn Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = 3 cos x + sin x182views
Textbook QuestionIn Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = cos x + cos 2x237views
Textbook QuestionIn Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = cos x + sin 2x209views
Textbook QuestionIn Exercises 67–68, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 4. y = cos πx + sin π/2 x190views
Textbook QuestionIn Exercises 79–82, graph f, g, and h in the same rectangular coordinate system for 0 ≤ x ≤ 2π. Obtain the graph of h by adding or subtracting the corresponding y-coordinates on the graphs of f and g. f(x) = 2 cos x, g(x) = cos 2x, h(x) = (f + g)(x)198views
Textbook QuestionIn Exercises 79–82, graph f, g, and h in the same rectangular coordinate system for 0 ≤ x ≤ 2π. Obtain the graph of h by adding or subtracting the corresponding y-coordinates on the graphs of f and g. f(x) = cos x, g(x) = sin 2x, h(x) = (f − g)(x)196views
Textbook QuestionIn Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −2 sin(2πx + 4π)22views
Textbook QuestionIn Exercises 31–34, determine the amplitude of each function. Then graph the function and y = cos x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 2 cos x20views
Textbook QuestionIn Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = cos 2x23views
Textbook QuestionIn Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = 4 cos 2πx21views
Textbook QuestionIn Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = -4 cos 1/2 x22views
Textbook QuestionIn Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = cos(x − π/2)22views
Textbook QuestionIn Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 3 cos(2x − π)24views
Textbook QuestionIn Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 1/2 cos (3x + π/2)19views
Textbook QuestionIn Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 cos (2x − π/2)23views
Textbook QuestionIn Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 2 cos (2πx + 8π)22views
Textbook QuestionIn Exercises 1–6, determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin 4x22views
Textbook QuestionIn Exercises 1–6, determine the amplitude and period of each function. Then graph one period of the function. y = 1/2 sin π/3 x22views
Textbook QuestionIn Exercises 7–11, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 cos (x + π)23views
Textbook QuestionIn Exercises 7–11, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 sin(π/3 x − 3π)21views