Question

if y=√3 sin t+cost, then maximum value of y occurs when value of t is​

Answer 1

Answer:

π / 3

Explanation:

Given :

y = √ 3 sin t + cos t

Since t depend on y :

To find max. value of y :

= > d y / d x = 0

= > d y / d x = (√ 3 sin t + cos t )' = 0

= > √ 3 cos t - sin t = 0

r = √ ( ( √ 3 )² + 1² )  = 2

Dividing by 2 we get :

= > √ 3 / 2 cos t - 1 / 2 sin t = 0

= > cos t . cos π / 6 - sin t . sin π / 6 = 0

Using formula :

= > cos  A . cos B - sin A . sin B = cos ( A + B )

= > cos ( t + π / 6 ) = 0

Writing ' 0 ' as cos π / 2

= > cos ( t + π / 6 ) = cos π / 2

Comparing both side we get :

= > t + π / 6 = π / 2

= > t = π / 3

Therefore , value of t is π / 3.