Question

The coordinates of a point are (a sin alpha ,a cos alpha) .Find the distance from origin.​

Answer 1

Answer:

Distance = a

Use the distance formula.

Answer 2

Answer:

a

Step-by-step explanation:

✯✯Given✯✯

A point with coordinate(asinα,acosα).

☛ To Find:

    Distance of given point from origin(0,0).

➺Formulae to be known before solving question

• If two points having coordinate ($\sf\bold{x_{1} ,y_{1} }$) and ($\sf\bold{x_{2} ,y_{2} }$) are given then distance between these points are given by

        $\sf {Distance\:formula=\sqrt{(x_{2}-x_{1} ) ^{2}+(y_{2}-y_{1} ) ^{2} }}$

• $\sf{sin^{2} x+cos^{2}x=1}$

➳Solution:

  $\sf{Distance\:between\: origin\: and\: given\: point}$

    $=\sqrt{(asin\alpha-0) ^{2}+(acos\alpha-0 ) ^{2} }$

    $\sf=\sqrt{(asin\alpha)^{2}+(acos\alpha)^{2} }$

    $\sf=\sqrt{a^{2}sin^{2}\alpha+a^{2}cos^{2}\alpha^{2} }$

    $\sf=\sqrt{a^{2}(sin^{2}\alpha+cos^{2}\alpha) }$

    $\sf=\sqrt{a^{2}(1) }$  

    $\sf=\sqrt{a^{2} }$

    $\sf\red{=a }$

$\sf\bold{Hence, distance\:between\:origin\:and\:given\:point\:is\:'a'.}$