6.1 Graphs of the Sine and Cosine Functions Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 1 -4 -3 -2 -1 -1 1 2 3 4 -2 -3 -4 -5 -6 -7 -8 -9 Based on the graph above, determine the amplitude, midline, and period of the function Amplitude: Period: Midline: y = #2 Points possible: 1. Total attempts: 3 Given the equation y = 3 sin(2(x + 6)) + 5 The amplitude is: The period is: The horizontal shift is: units to the Select an answer units to the Select an answer The midline is: y = #3 Points possible: 1. Total attempts: 3 Given the equation y = 6 sin(7x 21) + 5 The amplitude is: The period is: The horizontal shift is: The midline is: y = #4 Points possible: 1. Total attempts: 3 Find a function of the form y = A sin(kx) + C or y = A cos(kx) + C whose graph matches the function shown below: 5 4 3 2 1 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 -1 2 3 4 5 6 7 -2 -3 -4 -5 Leave your answer in exact form; if necessary, type pi for . y= #5 Points possible: 1. Total attempts: 3 Find a function of the form y = A sin(kx) + C or y = A cos(kx) + C whose graph matches the function shown below: 10 9 8 7 6 5 4 3 2 1 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 -2 -3 -4 -5 -6 -7 -8 -9 -10 Leave your answer in exact form; if necessary, type pi for . y= 4 5 6 7 8 9 10 11 #6 Points possible: 1. Total attempts: 3 2 1 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -1 -2 The curve above is the graph of a sinusoidal function. It goes through the points ( 8, 0) and (2, 0). Find a sinusoidal function that matches the given graph. If needed, you can enter =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = #7 Points possible: 1. Total attempts: 3 Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 50 degrees at midnight and the high and low temperature during the day are 58 and 42 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t) = #8 Points possible: 1. Total attempts: 3 A ferris wheel is 40 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters What is the Midline? y = meters What is the Period? y = minutes How High are you off of the ground after 3 minutes? meters #9 Points possible: 1. Total attempts: 3 A ferris wheel is 30 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t). f(t) = #10 Points possible: 1. Total attempts: 3 Sketch a graph of the function f(x) = sin(x). Assignment 6.2 Graphs of the Other Trigonometric Functions Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Given the equation y = 2 tan(6x + 48) The period is: The horizontal shift is: units to the Select an answer #2 Points possible: 1. Total attempts: 3 On the interval [0, 2) determine which angles are not in the domain of the tangent function, f() = tan() What angles are NOT in the domain of the tangent function on the given interval? #3 Points possible: 1. Total attempts: 3 On the interval [0, 2) determine which angles are not in the domain of the given functions. What angles are NOT in the domain of the secant function on the given interval? What angles are NOT in the domain of the cosecant function on the given interval? #4 Points possible: 1. Total attempts: 3 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 The graph above is a graph of what function? y = csc(x) y = cot(x) y = sin(x) y = sec(x) y = tan(x) y = cos(x) #5 Points possible: 1. Total attempts: 3 Match each graph with its equation. Not all equations will be used. 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 - -3 1 2 3 4 5 6 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 -1 -2 - -3 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 - -3 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 - -3 #6 Points possible: 1. Total attempts: 3 What is the period of the graph of the function y = sec( period = Enter answer as a fraction, not as a decimal. And, use pi for . 7x )? 6 #7 Points possible: 1. Total attempts: 3 Given the equation y = 4 tan(3x + 24) The period is: The horizontal shift is: units to the Select an answer units to the Select an answer #8 Points possible: 1. Total attempts: 3 Given the equation y = 8 sec(3x 6) The period is: The horizontal shift is: #9 Points possible: 1. Total attempts: 3 8 7 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 -2 -3 -4 -5 -6 -7 -8 Write an equation for the function graphed above. y= #10 Points possible: 1. Total attempts: 3 8 7 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 -2 -3 -4 -5 -6 -7 -8 Write an equation for the graph above. f(x) = 5 6 Assignment 6.3 Inverse Trigonometric Functions Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Evaluate the following expressions. Your answer must be an angle in radians and in the interval [ , ]. 2 2 (a) sin 1 (0) = (b) sin 1 ( 3 )= 2 (c) sin 1 ( 2 )= 2 #2 Points possible: 1. Total attempts: 3 Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval [0, ]. Example: Enter pi/6 for . 6 (a) cos 1 ( 3 )= 2 (b) cos 1 (0) = (c) cos 1 (1) = #3 Points possible: 1. Total attempts: 3 Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval [ , ]. Example: Enter pi/6 for . 6 2 2 (a) tan 1 ( 3 )= 3 (b) tan 1 (0) = (c) tan 1 ( 1) = #4 Points possible: 1. Total attempts: 3 b Find a simplified expression for cos(tan 1 ( )) 7 #5 Points possible: 1. Total attempts: 3 2 Evaluate cos(tan 1 ( )), giving your answer as an exact value (no decimals) 5 #6 Points possible: 1. Total attempts: 3 For the right triangle below, find the measure of the angle. Figure is not to scale. 12 <-- ? 9 degrees #7 Points possible: 1. Total attempts: 3 Evaluate the expression sin 1 (cos( 5 )). 6 Give your answer as an exact value #8 Points possible: 1. Total attempts: 3 Evaluate the expression cos 1 (sin( Give your answer as an exact value )). 4 #9 Points possible: 1. Total attempts: 3 b Find a simplified expression for tan(sin 1 ( )) 5 #10 Points possible: 1. Total attempts: 3 Use your calculator to evaluate cos 1 (0.5) to at least 3 decimal places Chapter 6 Review Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 -1 1 2 3 4 5 Based on the graph above, determine the amplitude, midline, and period of the function Amplitude: Period: Midline: y = #2 Points possible: 1. Total attempts: 3 Given the equation y = 4 sin(7(x 2)) + 8 The amplitude is: The period is: The horizontal shift is: units to the Select an answer units to the Select an answer The midline is: y = #3 Points possible: 1. Total attempts: 3 Given the equation y = 3 sin(8x 48) + 7 The amplitude is: The period is: The horizontal shift is: The midline is: y = #4 Points possible: 1. Total attempts: 3 Find a function of the form y = A sin(kx) + C or y = A cos(kx) + C whose graph matches the function shown below: 4 3 2 1 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 -2 -3 -4 Leave your answer in exact form; if necessary, type pi for . y= #5 Points possible: 1. Total attempts: 3 Find a function of the form y = A sin(kx) + C or y = A cos(kx) + C whose graph matches the function shown below: 4 3 2 1 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 -2 -3 -4 Leave your answer in exact form; if necessary, type pi for . y= 2 3 4 5 6 7 #6 Points possible: 1. Total attempts: 3 5 4 3 2 1 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 -2 -3 -4 -5 The curve above is the graph of a sinusoidal function. It goes through the points ( 8, 0) and (2, 0). Find a sinusoidal function that matches the given graph. If needed, you can enter =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = #7 Points possible: 1. Total attempts: 3 Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 80 degrees at midnight and the high and low temperature during the day are 86 and 74 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t) = #8 Points possible: 1. Total attempts: 3 A ferris wheel is 45 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters What is the Midline? y = meters What is the Period? y = minutes How High are you off of the ground after 4 minutes? meters #9 Points possible: 1. Total attempts: 3 A ferris wheel is 10 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t). f(t) = #10 Points possible: 1. Total attempts: 3 Sketch a graph of the function f(x) = sin(x). #11 Points possible: 1. Total attempts: 3 Given the equation y = 2 tan(3x + 12) The period is: The horizontal shift is: units to the Select an answer #12 Points possible: 1. Total attempts: 3 On the interval [0, 2) determine which angles are not in the domain of the tangent function, f() = tan() What angles are NOT in the domain of the tangent function on the given interval? #13 Points possible: 1. Total attempts: 3 On the interval [0, 2) determine which angles are not in the domain of the given functions. What angles are NOT in the domain of the secant function on the given interval? What angles are NOT in the domain of the cosecant function on the given interval? #14 Points possible: 1. Total attempts: 3 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 The graph above is a graph of what function? y = cot(x) y = csc(x) y = sin(x) y = cos(x) y = sec(x) y = tan(x) #15 Points possible: 1. Total attempts: 3 Match each graph with its equation. Not all equations will be used. 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 - -3 1 2 3 4 5 6 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 -1 -2 - -3 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 - -3 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 - -3 #16 Points possible: 1. Total attempts: 3 What is the period of the graph of the function y = cot( period = Enter answer as a fraction, not as a decimal. And, use pi for . 9x )? 17 #17 Points possible: 1. Total attempts: 3 Given the equation y = 3 tan(5x + 10) The period is: The horizontal shift is: units to the Select an answer units to the Select an answer #18 Points possible: 1. Total attempts: 3 Given the equation y = 8 sec(4x 28) The period is: The horizontal shift is: #19 Points possible: 1. Total attempts: 3 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 -2 -3 -4 -5 -6 Write an equation for the function graphed above. y= #20 Points possible: 1. Total attempts: 3 8 7 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 -2 -3 -4 -5 -6 -7 -8 Write an equation for the graph above. f(x) = #21 Points possible: 1. Total attempts: 3 Evaluate the following expressions. Your answer must be an angle in radians and in the interval [ , ]. 2 2 (a) sin 1 ( 3 )= 2 (b) sin 1 (1) = (c) sin 1 ( 2 )= 2 #22 Points possible: 1. Total attempts: 3 Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval [0, ]. Example: Enter pi/6 for . 6 (a) cos 1 (0) = (b) cos 1 ( 1 )= 2 1 (c) cos 1 ( ) = 2 #23 Points possible: 1. Total attempts: 3 Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval [ , ]. Example: Enter pi/6 for . 6 2 2 (a) tan 1 ( 1) = (b) tan 1 ( 3 )= 3 (c) tan 1 (1) = #24 Points possible: 1. Total attempts: 3 Find a simplified expression for tan(sin 1 ( y )) 10 #25 Points possible: 1. Total attempts: 3 Evaluate cos(tan 1 ( 11 )), giving your answer as an exact value (no decimals) 12 #26 Points possible: 1. Total attempts: 3 For the right triangle below, find the measure of the angle. Figure is not to scale. 10 <-- ? 12 degrees #27 Points possible: 1. Total attempts: 3 Evaluate the expression sin 1 (cos( 7 )). 4 Give your answer as an exact value #28 Points possible: 1. Total attempts: 3 Evaluate the expression cos 1 (sin( )). 4 Give your answer as an exact value #29 Points possible: 1. Total attempts: 3 t Find a simplified expression for sin(cos 1 ( )) 4 #30 Points possible: 1. Total attempts: 3 Use your calculator to evaluate cos 1 ( 0.49) to at least 3 decimal places Test 2 Name: Syd Hendricks #1 Points possible: 2. Total attempts: 1 Given the equation y = 5 sin(4(x 7)) + 6 The amplitude is: The period is: The horizontal shift is: units to the Select an answer units to the Select an answer The midline is: y = #2 Points possible: 2. Total attempts: 1 Given the equation y = 4 sin(7x 14) + 6 The amplitude is: The period is: The horizontal shift is: The midline is: y = #3 Points possible: 2. Total attempts: 1 Find a function of the form y = A sin(kx) + C or y = A cos(kx) + C whose graph matches the function shown below: 4 3 2 1 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 -2 -3 -4 Leave your answer in exact form; if necessary, type pi for . y= 4 5 6 7 8 9 10 11 #4 Points possible: 2. Total attempts: 1 2 1 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 -1 -2 The curve above is the graph of a sinusoidal function. It goes through the points ( 4, 0) and (2, 0). Find a sinusoidal function that matches the given graph. If needed, you can enter =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = #5 Points possible: 2. Total attempts: 1 A ferris wheel is 50 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t). f(t) = #6 Points possible: 2. Total attempts: 1 Sketch a graph of the function f(x) = sin(x). #7 Points possible: 2. Total attempts: 1 Given the equation y = 2 tan(4x + 32) The period is: The horizontal shift is: units to the Select an answer #8 Points possible: 2. Total attempts: 1 On the interval [0, 2) determine which angles are not in the domain of the tangent function, f() = tan() What angles are NOT in the domain of the tangent function on the given interval? #9 Points possible: 2. Total attempts: 1 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 The graph above is a graph of what function? y = csc(x) y = cot(x) y = cos(x) y = tan(x) y = sec(x) y = sin(x) #10 Points possible: 2. Total attempts: 1 What is the period of the graph of the function y = sec( 5x )? 21 period = Enter answer as a fraction, not as a decimal. And, use pi for . #11 Points possible: 2. Total attempts: 1 Given the equation y = 5 sec(3x 18) The period is: The horizontal shift is: units to the #12 Points possible: 2. Total attempts: 1 8 7 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 -2 -3 -4 -5 -6 -7 -8 Write an equation for the graph above. f(x) = 5 6 Select an answer #13 Points possible: 2. Total attempts: 1 Evaluate the following expressions. Your answer must be an angle in radians and in the interval [ , ]. 2 2 (a) sin 1 2 ( )= 2 (b) sin 1 ( 2 )= 2 (c) sin 1 (1) = #14 Points possible: 2. Total attempts: 1 Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval [0, ]. Example: Enter pi/6 for . 6 (a) cos 1 ( 2 )= 2 (b) cos 1 ( 1 )= 2 (c) cos 1 ( 3 )= 2 #15 Points possible: 2. Total attempts: 1 Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval [ , ]. Example: Enter pi/6 for . 6 2 2 (a) tan 1 (3) = (b) tan 1 (0) = (c) tan 1 (1) = #16 Points possible: 2. Total attempts: 1 a Find a simplified expression for tan(cos 1 ( )) 4 #17 Points possible: 2. Total attempts: 1 1 Evaluate cos(tan 1 ( )), giving your answer as an exact value (no decimals) 6 #18 Points possible: 2. Total attempts: 1 For the right triangle below, find the measure of the angle. Figure is not to scale. 6 <-- ? 7 degrees #19 Points possible: 2. Total attempts: 1 Evaluate the expression sin 1 (cos( 2 )). 3 Give your answer as an exact value #20 Points possible: 2. Total attempts: 1 Evaluate the expression cos 1 (sin( Give your answer as an exact value )). 3 \f\f\f\f \f\f\f\f