(cos2(cos(cos t)))

Question

I dont know how to answer this problem so i would like to have someone work it out thanks.

Answer 1

cos²(cos(cos(t))) is a periodic function with period π (180°).

Its amplitude is:

½(cos²(cos(cos(π)))-cos²(cos(cos(π/2))))=½(0.735398-0.291927)=0.221736 (approx).

Here's a table of values showing maxima at t=0, π, and minimum at t=½π. The function is symmetrical about t=0, and you can see the symmetry in the interval [0,π], on either side of t=½π.

t	cos2(cos(cos(t)))
0	0.735398
0.1π (18°)	0.698915
0.2π (36°)	0.594614
0.3π (54°)	0.453296
0.4π (72°)	0.335865
½π (90°)	0.291927
0.6π (108°)	0.335865
0.7π (126°)	0.453296
0.8π (144°)	0.594614
0.9π (162°)	0.698915
π (180°)	0.735398