2 The height of the first part of a rollercoaster track is \(h \mathrm {~m}\) at a horizontal distance of \(x \mathrm {~m}\) from the start. A student models this using the equation \(h = 17 + 15 \cos 6 x\), for \(0 \leqslant x \leqslant 40\), using the values of \(h\) given when their calculator is set to work in degrees.
- Find the height that the student's model predicts when the horizontal distance from the start is 40 m .
- The student argues that the model predicts that the rollercoaster track will achieve a maximum height of 32 m more than once because the cosine function is periodic.
Comment on the validity of the student's argument.