Answer to Question #103877 in Trigonometry for Martin

Question

(1 point) If k≥1, the graphs of y=sinx and y=ke−x intersect for x≥0. Find the smallest value of k for which the graphs are tangent.

Answer 1

y=f'(x₀) *(x-x₀) +f(x₀)

y=cos(x₀) *(x-x₀) +sin(x₀)

cos(x₀) =-1

x₀=π+2πn

for n=0:

y=ke-π=sin(π) =0

k=π/e