IB Maths AA HL Ahl 3 9 Hl Reciprocal and Inverse Trigonometric Functions Questions

Practise IB Mathematics HL 3.9 by applying reciprocal and inverse trigonometric functions methods to questions from the Question Bank.

Exam points

Define sec θ, cosec θ and cot θ and apply 1 + tan²θ = sec²θ or 1 + cot²θ = cosec²θ to simplify and solve trigonometric expressions.
Use the domains, ranges and graphs of arcsin x, arccos x and arctan x to interpret inverse-trigonometric values and solve bounded problems.

[Maximum number: 1]

Two boats A and B travel due north.
Initially, boat B is positioned 50 metres due east of boat A .
The distances travelled by boat A and boat B , after t seconds, are x metres and y metres respectively. The angle $\theta$ is the radian measure of the bearing of boat B from boat A . This information is shown on the following diagram.

Figure for Question IB Maths AA HL Ahl 3 9 Hl Reciprocal and Inverse Trigonometric Functions Questions question 1 — IB Maths AA HL

Show that $y=x+50 \cot \theta$ .

At time T, the following conditions are true.
Boat B has travelled 10 metres further than boat A .
Boat B is travelling at double the speed of boat A .
The rate of change of the angle $\theta$ is -0.1 radians per second.

$\tan \theta=\frac{50}{y-x}$ OR $\cot \theta=\frac{y-x}{50}$ $y=x+50 \cot \theta$
AG
Note: y-x may be identified as a length on a diagram, and not written explicitly.

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IB Maths AA HL Ahl 3 9 Hl Reciprocal and Inverse Trigonometric Functions Questions question 1