at the start, object is 4 metres from the fixed point.ģ0 Model: The motion of an object oscillates such that its displacement, s, from a fixed point is given by s = 4cos3t where s is in meters and t is in seconds. (a) How far from the fixed point is the object at the start? At the start, t = 0 When t = 0, s = 4 cos(3x0) = 4 cos0 = 4 x 1 = 4 i.e. (a) How far from the fixed point is the object at the start? (b) How long does it take for the object to return to its starting point? (c) Find the object’s velocity (i) at the start (ii) as it passes the fixed point (iii) after 2 sec (d) Find its acceleration as it passes the fixed pointĢ9 Model: The motion of an object oscillates such that its displacement, s, from a fixed point is given by s = 4cos3t where s is in meters and t is in seconds. 1m 0m -1m s = cos t v = -sin t a = -cos tĢ8 Model: The motion of an object oscillates such that its displacement, s, from a fixed point is given by s = 4cos3t where s is in meters and t is in seconds. 1(a,b,d,f,h,j), 3 – 8 (all) FM Ex 19.5 1,4,5Ģ5 Model : Find the gradient of the curve y = sin 2x at the point where x = π/3Ģ6 Model : Find the gradient of the curve y = sin 2x at the point where x = π/3Ĭonsider the motion of an object on the end of a spring dropped from a height of 1m above the equilibrium point which takes 2π seconds to return to the starting point. Model : Find the derivative of (a) sin 2x (b) sin32x (c) sin2x cos3x (d) sin(π-3x) _ (d) y = sin (π-3x) = sin 3x dy = 3 cos 3x dxĢ4 NEWQ P50 2.4 No. Model : Find the derivative of (a) sin 2x (b) sin32x (c) sin2x cos3x (d) sin(π-3x) _ (c) y = sin2x cos3x = uv where u = sin2x and v = cos3x du = 2 sinx cosx dv = -3 sin3x dx dx dy = u dv + v du dx dx dx = -3 sin3x sin2x + cos3x 2 sin x cos x = -3 sin3x sin2x + 2 cos3x sin x cos xĢ3 _ Model : Find the derivative of (a) sin 2x (b) sin32x (c) sin2x cos3x (d) sin(π-3x) _ (b) y = sin32x ( = (sin 2x)3 ) = u3 where u = sin 2x dy = 3u du = 2 cos 2x du dx dy = dy. Model : Find the derivative of (a) sin 2x (b) sin32x (c) sin2x cos3x (d) sin(π-3x) _ (a) y = sin 2x = sin u where u = 2x dy = cos u du = 2 du dx dy = dy. Y = sin x dy = cos x dx y = cos x dy = -sin x dxġ9 Model : Find the derivative of (a) sin 2x (b) sin32x (c) sin2x cos3x (d) sin(π-3x)Ģ0 _ Tan is negative angle is in Q2 or Q4 (b) tan x = -1 x = 180 - 45 or x = 360 - 45 = or 45 45° Value of tan x is -1 45 off x-axisħ New Q Ex 10.3 Page ,6 FM Page Ex (orally)Ĭos θ = 0.643 θ = cos-1 (0.643) θ ≈ 50° But cos 310° = also So there appears to be more than one solution So, how many solutions are there?ĩ θ = 50° + 360° x n θ = 310° + 360° x n y=0.643 cos curve cos θ = 0.634 Modelğind all values of x (to the nearest minute) where 0< x <360 for which (a) sin x = 0.5 (b) tan x = -1ĥ (a) sin x = 0.5 x = 30 or x = 180 - 30 = 30 or 150
REVISION New Q Ex 10.1 No (parts a & b only), leave out no.10 FM Page Ex 5.8 Significance of the constants A,B,C and D on the graphs of y = A sin(Bx+C) + D, y = A cos(Bx+C) + D Application of periodic functions Solution of simple trig equations within a specified domain Derivatives of functions involving sin x and cos x Applications of the derivatives of sin x and cos x in life-related situationsĢ Periodic Functions And Applications IIIģ No. 1 Periodic Functions And Applications III
0 kommentar(er)
