1-if-sin-x-k-sin-find-tan-and-k-then-find-in-0-2pi-when-k-1-2-and-pi-2-if-x-sin-t-and-y-cos-2t-show-that-d-2-y-dx-2-4-0-

Question Number 86041 by M±th+et£s last updated on 26/Mar/20

1) i f

s i n (θ - x) = k s i n (θ + α)

f i n d t a n (θ) a n d k

t h e n f i n d θ i n [0, 2 π] w h e n k = \frac{1}{2} a n d α = π

2) i f x = s i n (t) a n d y = c o s (2 t)

s h o w t h a t

\frac{d^{2} y}{{d x}^{2}} + 4 = 0

Answered by Rio Michael last updated on 26/Mar/20

2) x = \sin t and y = \cos (2 t)

\Rightarrow \frac{d x}{d t} = \cos t and \frac{d y}{d t} = - 2 \sin (2 t)

\Rightarrow \frac{d y}{d x} = \frac{d y}{d t} . \frac{d t}{d x} = \frac{- 2 \sin (2 t)}{\cos t} = \frac{- 2 (2 \sin t \cos t)}{\cos t} = - 4 \sin t

\frac{d^{2} y}{{d x}^{2}} = \frac{d}{d x} (\frac{d y}{d x}) \frac{d t}{d x} = - 4 \cos t \times \frac{1}{\cos t} = - 4

\Rightarrow \frac{d^{2} y}{{d x}^{2}} = - 4 hence \frac{d^{2} y}{{d x}^{2}} + 4 = 0

Commented by M±th+et£s last updated on 26/Mar/20

g o d b l e s s y o u

Answered by mind is power last updated on 27/Mar/20

s i n (θ - α) = k s i n (θ + α) . . Q u a t i o n 1 ?

Commented by M±th+et£s last updated on 27/Mar/20

y e s s i r