IB Maths AA HL AA 3.2 Radians and circular functions questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Paper 1, no calculator Paper 2, calculator

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Question 1

Paper 2, calculatorEasy5 marks

A simplified model for the water depth at a harbour is

h(t)=2.4+1.6\sin\left(\frac{\pi}{6}(t-2)\right),

where $h$ is measured in metres and $t$ is the number of hours after midnight.

(a)

State the amplitude and the midline height of the model.

[2]

(b)

Determine the period of the model.

[1]

(c)

Calculate the water depth at $t=5$

[2]

Question 2

Paper 1, no calculatorMedium6 marks

In triangle $ABC$ the sides $a$ $b$ and $c$ are opposite the angles $A$ $B$ and $C$ respectively. Angles are measured in radians.

It is given that $A=\frac{\pi}{6}$ $a=6$ and $b=6\sqrt{3}$

(a)

Determine all possible values of $B$

[2]

(b)

Hence determine the corresponding values of $C$

[2]

(c)

For the obtuse value of $B$ determine the exact value of $\tan B$

[2]

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