Senior Secondary (HKDSE) · Mathematics

More about Trigonometry: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on More about Trigonometry.

10 questions27 marksFree, no account

Question 1

1 mark

Consider the trigonometric function \(y = 3 - 2 \sin(4x - 60^{\circ})\). Which of the following is the maximum value of the function?

Question 2

1 mark

The figure shows a right pyramid with a square base \(ABCD\) of side length \(10 \text{ cm}\). The vertex \(V\) is located such that the foot of the perpendicular from \(V\) to the base is the center of the square. If the height of the pyramid is \(12 \text{ cm}\), find the angle between the slant edge \(VA\) and the base \(ABCD\) correct to the nearest degree.

Question 3

1 mark

Find the maximum value of the function \(f(\theta) = 4\sin^2 \theta + 6\cos \theta + 3\) for \(0^\circ \le \theta < 360^\circ\).

Question 4

1 mark

Consider the function \(y = 4 - 3\sin \theta\) for \(0^{\circ} \le \theta \le 360^{\circ}\). Find the range of the function.

Question 5

1 mark

Solve the trigonometric equation \(2 \tan \theta = \sin \theta\) for \(0^\circ \le \theta < 360^\circ\).

Question 6

3 marks

In \(\triangle ABC\), the lengths of sides \(AB\), \(BC\) and \(AC\) are \(13\text{ cm}\), \(14\text{ cm}\) and \(15\text{ cm}\) respectively. Use Heron's formula to find the area of \(\triangle ABC\).

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

In a cube \(ABCD-EFGH\), where \(ABCD\) is the horizontal base and \(E, F, G, H\) are vertices directly above \(A, B, C, D\) respectively, find the angle between the body diagonal \(HB\) and the base \(ABCD\), correct to 1 decimal place.

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

In a right triangular prism \( ABC-DEF \), the base \( ABC \) is an equilateral triangle with side length \( 4 \) cm and the height of the prism is \( 6 \) cm. If \( M \) is the midpoint of the edge \( EF \), find the angle between the line \( AM \) and the base \( ABC \) correct to the nearest \( 0.1^\circ \).

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Question 9

5 marks

In \(\triangle PQR\), \(PQ = 15\text{ cm}\), \(\angle QPR = 35^\circ\) and \(\angle PQR = 75^\circ\).

(a) Find \(\angle PRQ\).

(b) Find the length of \(QR\) correct to 3 significant figures.

(c) Find the area of \(\triangle PQR\) correct to 3 significant figures.

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

A vertical pole \(OP\) stands at the corner \(O\) of a horizontal rectangular field \(OABC\). It is given that \(OA = 5\text{ m}\) and \(OC = 12\text{ m}\). The angle of elevation of the top of the pole \(P\) from the vertex \(B\) is \(30^\circ\).

(a) Find the length of the diagonal \(OB\).

(b) Find the height of the pole \(OP\) in metres, leaving your answer in surd form.

(c) Find the angle of elevation of \(P\) from vertex \(A\), correct to 1 decimal place.

Write your answer out first, then check it against the worked solution.

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