Find to three decimal places the coordinate of point P lying

Find to three decimal places, the coordinate of point P lying in the 4th quadrant on the Cartesian plan such that the line tangent to the cosine function passes through the origin. X:[0,2Pi] Show all work and describe all steps.

Solution

t = cos x

tangent passing through origin

t\' = -sin x

So,

tangent y = mx+c

y = -xsinx+c

here,

(0,0) is point on tangent,

0 = -0sin0 + c

c = 0

So,

y = -xsinx is tangent.