I'm asked to find the the times (0<t<2pi) that two vectors are perpendicular.
The two vectors are perpendicular when their Dot product is zero. Taking the Dot product, and equating to zero gives:
2.Cos(2t).Sin(2t) - 4.Cos(t).Sin(t)=0
So the vectors are perpendicular when the above holds true.
I've sketched the plot of Sin(t), Cos(t), Sin(2t) and Cos(2t).
The R.H.S. of the equation reduces to zero when either Cos(t) or Sin(t) are zero, this is at ;
t=0, pi/2, pi, 3pi/2, 2pi, and the above equation holds true.
I feel like I've done this more by intuition than by mathematical method, and I can't show that these are the only values for which the vectors are perpendicular (though I suspect they are).
There must be a better way to go about this, and I have a feeling it may be with some trig identity.
In short, have I got all the values? Is there a better way to do it?