F.IF.B.4 Graphing Trigonometric Functions

Transcription

1 F.IF.B.4 Graphing Trigonometric Functions The maximum value of the function y sinx is ) ) ) 4) What is the minimum value of f() in the equation f() sin4? ) ) ) 4) 4 What is the maximum value for the function y sin5x is: ) ) ) 5 4) 5 4 If f(x) sinx C, then the maximum value of f(x) is: ) C ) C ) C 4) C 6 6 The path traveled by a roller coaster is modeled by the equation y 7sinx 0. What is the maximum altitude of the roller coaster? ) ) 7 ) 0 4) 57 7 The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation. The height, H, in feet, above the ground of one of the six-person cars can be modeled by H(t) 70sin ( t.75) 80, where t is time, 7 in minutes. Using H(t) for one full rotation, this car's minimum height, in feet, is ) 50 ) 70 ) 0 4) 0 8 Which function's graph has a period of 8 and reaches a maximum height of if at least one full period is graphed? ) y 4cos 4 x ) y 4cos 4 x 5 ) y 4cos(8x) 4) y 4cos(8x) 5 5 What is the maximum value of y for the equation y sinx? ) ) ) 4) 4

2 9 Based on climate data that have been collected in Bar Harbor, Maine, the average monthly temperature, in degrees F, can be modeled by the equation B(x).94sin(0.508x.6) The same governmental agency collected average monthly temperature data for Phoenix, Arizona, and found the temperatures could be modeled by the equation P(x) 0.8sin(0.55x.48) Which statement can not be concluded based on the average monthly temperature models x months after starting data collection? ) The average monthly temperature variation is more in Bar Harbor than in Phoenix. ) The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix. ) The maximum average monthly temperature for Bar Harbor is 79 F, to the nearest degree. 4) The minimum average monthly temperature for Phoenix is 0 F, to the nearest degree. 0 Relative to the graph of y sinx, what is the shift of the graph of y sin x? ) right ) left ) up 4) down Given the parent function p(x) cosx, which phrase best describes the transformation used to obtain the graph of g(x) cos(x a) b, if a and b are positive constants? ) right a units, up b units ) right a units, down b units ) left a units, up b units 4) left a units, down b units Which transformation could be used to make the graph of the equation y sinx coincide with the graph of the equation y cosx? ) translation ) rotation ) dilation 4) point reflection The graph of the equation y sinx will contain no points in Quadrants ) I and II ) II and III ) III and IV 4) I and IV 4 Which type of symmetry does the equation y = cos x have? ) line symmetry with respect to the x-axis ) line symmetry with respect to y x ) point symmetry with respect to the origin 4) point symmetry with respect to,0 5 The graph of which equation is symmetric with respect to the origin? ) y ) x ) y sinx 4) y cosx 6 As angle x increases from 80º to 70º, the value of cosx will ) increase from 0 to ) increase from to 0 ) decrease from 0 to 4) decrease from to 0

3 7 As increases from to, which statement is true? ) Sin increases from to 0. ) Sin decreases from to 0. ) Cos decreases from 0 to. 4) Cos increases from to 0. A sine function increasing through the origin can be used to model light waves. Violet light has a wavelength of 400 nanometers. Over which interval is the height of the wave decreasing, only? ) (0,00) ) (00,00) ) (00,400) 4) (00,400) 8 As increases from to, the value of cos ) decreases, only ) increases, only ) decreases and then increases 4) increases and then decreases 9 As angle x increases from to, the value of sinx will ) increase from to 0 ) increase from 0 to ) decrease from 0 to 4) decrease from to 0 0 As x increases from to, the value of sinx ) increases, only ) decreases, only ) increases, then decreases 4) decreases, then increases As x increases from 0 to, the graph of the equation y tanx will ) increase from 0 to ) decrease from 0 to ) increase without limit 4) decrease without limit 4 The height, h(t) in cm, of a piston, is given by the equation h(t) cos t 8, where t represents the number of seconds since the measurements began. Determine the average rate of change, in cm/sec, of the piston's height on the interval t. At what value(s) of t, to the nearest tenth of a second, does h(t) 0 in the interval t 5? Justify your answer. As angle increases from radians to radians, the cosine of ) increases throughout the interval ) decreases throughout the interval ) increases, then decreases 4) decreases, then increases

4 ID: A F.IF.B.4 Graphing Trigonometric Functions Answer Section ANS: REF: 0685siii ANS: REF: 0895siii ANS: REF: 08940siii 4 ANS: The maximum of a sine wave is. () C C. REF: fall999b 5 ANS: 4 REF: 090siii 6 ANS: 4 The maximum of a sine wave is. 7() REF: 08049b 7 ANS: REF: 066aii 8 ANS: 4() 8 b H(t) is at a minimum at 70() 80 0 b 4 REF: 0880aii 9 ANS: 4 Bar Harbor Phoenix Minimum Midline Maximum Range REF: 0675aii 0 ANS: REF: 070aii ANS: 4 REF: 06706aii ANS: REF: 007b ANS: REF: 08090b 4 ANS: 4 REF: 006b 5 ANS: REF: 0899siii 6 ANS: REF: 068siii

5 ID: A 7 ANS: 4 REF: 06854siii 8 ANS: REF: 08909siii 9 ANS: 4 REF: 06000siii 0 ANS: 4 REF: 08009siii ANS: REF: 0609siii ANS: REF: 0860aii ANS: REF: 08705aii 4 ANS: h() h(), h(t) 0 at t.,.8, using a graphing calculator to find where h(t) 0. REF: 0686aii