Harder 3U Question (1 Viewer)

[apollo1]

consider the pair of simultaneous equations:

y = sinxcosx
y = kx

(i) suppose k is positive. Find any restriction on k so that the equations will have a unique simultaneous solution.

(ii) Suppose k is negative. Show that the pair of equations have a unique simultaneous solution if k < cos u, where u satisfies the equation tan u = u for

 

[Drongoski]

i) y = sinxcosx = 0.5sin2x

Looking at its graph, k (>0) the gradient of y = kx must be > gradient of y = sinxcosx at x=0 which = 1. Therefore we need k > 1 in order for the straight line to intersect the graph of y = sinxcosx at only 1 point (viz. @ x = 0).