Question

if x=a cos theta and y=a sin theta, express x in terms of y ​

Answer 1

Answer:

y=a2sin2theeta

Step-by-step explanation:

x=acos theeta y=asin theeta

x2+y2=a2cos2 theeta +a2sin2 theeta

x2+y2=a2 (sin2 theeta+cos2 theeta)

x2+y2=a2

y2=a2-x2

y2=a2-a2cos2 theeta

y2=a2 (1-cos2 theeta)

y2=a2sin2 theeta

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

$\longmapsto$FORMULA TO BE IMPLEMENTED

${sin}^{2} \theta + {cos}^{2} \theta = 1$

$\longmapsto$CALCULATION

$x=a cos \theta \: \: and \: \: \: \: y=a sin \theta$

Therefore

${x}^{2} + {y}^{2}$

$= {(a \ \cos \theta ) }^{2} + {(a \ \sin \theta ) }^{2}$

$= {a}^{2} {sin}^{2} \theta + {a}^{2} {cos}^{2} \theta$

$= {a}^{2} ( {sin}^{2} \theta + {cos}^{2} \theta)$

$= {a}^{2} \times 1$

$= {a}^{2}$

So

${x}^{2} + {y}^{2} = {a}^{2}$

$\implies \: {x}^{2} = {a}^{2} - {y}^{2}$

$\therefore \: x \: = \sqrt{ {a}^{2} - {y}^{2} }$

Which is required relationship