Question

e) y_3cos(x +4) +4 MaxMinAmp riod f y 5 cos 2n(x -0.5)+5 V.T Max Amp Min AC SİNE function has a maximu m value of 4, aminimum value of 2, a phase shift of 1 rad to the right, and a period of 4. Write an equation for the function and graph the function [KU, 6m] 2. Min _Armp period. P.S V.T. . Equation 3. Determine the equation for the following a) COSINE function Equation b) SINE function Equation 4. A buoy bobs up and down in the lake. The distance between the highest and lowest points is 2 m. It takes 4s for the buoy to move from its highest point to its lowest point and back to its highest point. a) Model the vertical displacement, v, of the buoy as a SINE FUNCTION of time, t, in seconds. Assume that t oy is on its way down at that time [A, 3m] the buoy is at its maximum att0 s and that the bu Equation b) Sketch a graph of v versus t over two cycles A, 2m) The piston in the engine of a small aircraft moves horizontally relative to the crankshaft, from a minimum distance of 10 cm to a maximum distance of 70 cm. During normal cruise power settings, the piston completes 15 rpm (revolutions per minute). 5. a) Model the horizontal position, h, in centimetres, of the piston as a COSINE FUNCTION of time, t, in seconds. Assume that the piston is at its midpoint t at t0 and on its way down at that time. A, 3m] Equation c) Sketch a graph of v versus t over two cycles A, 2m) n the interval x jo,2n-angles must be in standard pesition m, 12m] lanswers as fractions) a) tan'x-0.9-0 c) secx-144 0 e) tan'x+5 tanx + 6-0 f) 4sin2x-10

Answer 1

(e)

ymał = 7 Ymin = 1 Amp = 6 period = 11

-10 -5 10 15

(f)

= 10 min-0 Arnp 10 period 1.5

15 10 -5 10 -15