Find the equations of the tangent and normal to the given curves at the indicated points: x = cos t, y = sin t at t=π/4

Question

Find the equations of the tangent and normal to the given curves at the indicated points: x = cos t, y = sin t at t=&pi;/4

Philoid · Accepted Answer

It is given that equation of curve is x = cost, y = sint

On differentiating with respect to x, we get

Therefore, the slope of the tangent at ) is -1.

When

Then, the equation of the tangent is is

y – = -1(x – )

⇒ x + y -- = 0

⇒ x + y - = 0

Then, slope of normal at

=

Now, equation of the normal at

y – = 1(x –)

⇒ x = y