1)if sin(θ−x)=k sin(θ+α) find tan(θ) and k then find θ in[0,2π] when k=(1/2) and α=π 2)if x=sin(t) and y=cos(2t) show that (d^2 y/dx^2 )+4=0


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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

	$y e s s i r$
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