trig question (1 Viewer)

[chunder]

a question in three parts:

(i) By sketching y=x and y=sinx on the same axes, give a reasoned explanation of how many roots the equaion sinx=x has.

(ii) Make a similar analysis for the equation sin(nu)=nu where "n" is a positive integer

(iii) For what positive integer values of "n" does the equation
sin(nv)=v have 3 real roots? Justify your answer

its the third part that is giving me the shits

 

[McLake]

(i) By sketching y=x and y=sinx on the same axes, give a reasoned explanation of how many roots the equaion sinx=x has.

Graph these two lines, the point of intersections are the roots.

(ii) Make a similar analysis for the equation sin(nu)=nu where "n" is a positive integer

Ok, this just allows for a couple of special casses (n = 0 for instance).

(iii) For what positive integer values of "n" does the equation
sin(nv)=v have 3 real roots? Justify your answer

For this one think about what amplitude the sin wave needs for the line y=x to cut it three times. Obviously this can only happen when it cuts the sin curve at maximum/minimum points (along with the origin).