6. Trigonometry

Applications — Quiz

Test your understanding of applications with 5 practice questions.

Practice Questions

Question 1

A ship sails 500 km on a bearing of $045^\circ$ and then 300 km on a bearing of $120^\circ$. What is the straight‐line distance from its starting point to its final position, to the nearest kilometre?

Question 2

Two points A and B on one bank of a river are 200 m apart. From A the angle to a tree on the opposite bank is $60^\circ$ and from B it is $50^\circ$. What is the distance from A to the tree, to the nearest metre?

Question 3

The tidal height at a pier is modelled by $H(t)=A\cos\!\bigl(\tfrac{\pi}{6}t\bigr)+D$, where $t$ is hours after midnight. If the maximum height is 6 m at $t=0$ and the minimum is 2 m at $t=6$, which model is correct?

Question 4

The day‐length in hours over a year can be modelled by $D(d)=4\cos\!\bigl(\tfrac{2\pi}{365}(d-C)\bigr)+12\,$, where $d$ is day number. If the longest day (16 h) is on day 172, what is the phase shift $C$?

Question 5

A sound wave travels at 240 m/s with wavelength 0.75 m. What is its angular frequency $\omega$ in rad/s?