By sketching a suitable pair of graphs, show that the equation
cosec x = (1/2)x+1
where x is in radians, has a root in the intervale 0

Question

By sketching a suitable pair of graphs, show that the equation 
cosec x = (1/2)x+1
where x is in radians, has a root in the intervale 0<x<(1/2) pi

anonymous · Answer

@.Sam.

anonymous · Answer

attachment

anonymous · Answer

This is Graph from -Pi to Pi

anonymous · Answer

How could you do this by plugging in values, since the calc doesn't have any cosec values?

anonymous · Answer

1/Sin(x)=csc(x)

anonymous · Answer

so it becomes 1/sin(x) = 1/2(x) +1?

anonymous · Answer

pretty much yeah

anonymous · Answer

but which is the y and which is the x value?

anonymous · Answer

plot cscx=y and the line y= 0.5x+1 on same graph...they will intersect in the interval given, to give a root..

.sam. · Answer

attachment

anonymous · Answer

but cscx=y is equivalent to 1/sin x=y?

anonymous · Answer

yeah

anonymous · Answer

OK, that makes more sense now :)

.sam. · Answer

You just sketch both sides then get the intersection