Question

please refer picture for question help me for answer​

Answer 1

Answer:

-1

Step-by-step explanation:

x = a cos○

y= a sin○

differentiating both with d○

dx = d a cos○ = -asin○

___ __________

d○ d○

dy = d a sin○ = a cos○

___ ___________

d○ d○

NOW dy/dx

dy a cos○ cos○

___ = _________ =_____ = -cot○

dx - a sin○ -sin○

At ○ = pi /4

pi

-cot __= -1

4

Answer 2

Question :–

• If $\: \: \: { \bold{x = a \cos( \theta) \: \: and \: \: y = a \sin( \theta) }}$ then find

${ \bold{ \dfrac{dy}{dx} \: \: at \: \: \theta = \dfrac{\pi}{4} }}$

ANSWER :–

▪︎$\to{ \bold{ [(\frac{dy}{dx}) _{ \theta = \frac{\pi}{4} }]= - 1 }}$

EXPLANATION :–

GIVEN :–

▪︎ ${ \bold{x = a \cos( \theta) \: \: and \: \: y = a \sin( \theta) }}$

TO FIND :–

▪︎ ${ \bold{ \dfrac{dy}{dx} \: \: at \: \: \theta = \dfrac{\pi}{4} }}$

SOLUTION :–

➨ $\implies{ \bold{y \: = a \sin( \theta) }}$

• Now Let's Differentiate 'y' with respect to ${ \bold{ \theta}}$ –

$\\ \implies{ \bold{ \dfrac{dy}{d \theta} = a \cos( \theta) }}$

➨ $\implies{ \bold{x\: = a \cos( \theta) }}$

• Now Let's Differentiate 'x' with respect to ${ \bold{ \theta}}$ –

$\\ \implies{ \bold{ \dfrac{dx}{d \theta} = - a \sin( \theta) }}$

☞ ${ \bold{ \dfrac{dy}{dx} = \frac{ \frac{dy}{d \theta} }{ \frac{dx}{d \theta} } }}$

$\\ \implies{ \bold{ \dfrac{dy}{dx} = \frac{a \cos( \theta) }{ - a \sin( \theta) } }}$

$\\ \implies{ \bold{ \dfrac{dy}{dx} = - \cot( \theta) }}$

▪︎ Now put ${ \bold{ \theta = \dfrac{\pi}{4} }}$ –

$\\ \implies{ \bold{ [(\frac{dy}{dx}) _{ \theta = \frac{\pi}{4} }]= - \cot( \frac{\pi}{4} ) }}$

$\\ \implies{ \bold{ [(\frac{dy}{dx}) _{ \theta = \frac{\pi}{4} }]= - 1 }}$

Hence , Option (d) is correct.