Answer to Question #198427 in Calculus for unofuego

Question

The point

(π/6 , 1/2)

is on a curve and at any point on the curve, the slope of the tangent line is given by

−2 sin(2x)

. Find an equation of the curve.

Answer 1

Given point is (π/6,1/2)

Given slope of tangent line is -2sin(2x)

So, dy/dx = -2sin(2x)

dy = -2sin(2x) dx

Integrating on both sides with respect to x

∫ dy = (-2) ∫ sin(2x) dx

y = (-2)(-1/2) cos(2x) + C

y = cos(2x) + C

Put (π/6,1/2) in above curve

(1/2) = cos(2*π/6) + C

(1/2) = (1/2) + C

C = 0

Thus, The equation of curve is y = cos(2x)