Trigonometry: practice questions

6 questions · 11 marks · free, no account · Read the notes first

1. Question 1Multiple choice · 1 mark

   Solve $2\sin\theta = 1$ for $0° \leq \theta < 360°$.

   A

   $30°$ only

   B

   $30°$ or $150°$

   C

   $30°$ or $330°$

   D

   $60°$ or $120°$

2. Question 2Multiple choice · 1 mark

   Simplify $\dfrac{1 - \cos^2\theta}{\sin\theta\cos\theta}$.

   A

   $\sin\theta$

   B

   $\dfrac{1}{\tan\theta}$

   C

   $\tan\theta$

   D

   $\cos\theta$

3. Question 3Multiple choice · 1 mark

   In $\triangle ABC$, $a = 7$, $b = 8$ and $C = 60°$. Find $c$.

   A

   $13$

   B

   $\sqrt{113}$

   C

   $7$

   D

   $\sqrt{57}$

4. Question 4Multiple choice · 1 mark

   Two sides of a triangle are 6 cm and 10 cm, and the angle between them is $150°$. Find the area of the triangle.

   A

   $15$ cm²

   B

   $30$ cm²

   C

   $15\sqrt{3}$ cm²

   D

   $26$ cm²

5. Question 53 marks

   In $\triangle ABC$, $\angle A = 40°$, $\angle B = 65°$ and $BC = 12$ cm. Find $AC$, correct to 3 significant figures.

   Show worked solution

   By the sine rule, $\dfrac{AC}{\sin 65°} = \dfrac{12}{\sin 40°}$ 1M

   $AC = \dfrac{12\sin 65°}{\sin 40°}$ 1M

   $\approx 16.9$ cm 1A

6. Question 64 marks

   The sides of a triangle are 5 cm, 7 cm and 8 cm.

   (a) Find the angle opposite the side of 7 cm.

   (b) Hence find the area of the triangle in surd form.

   Show worked solution

   (a) By the cosine rule, $\cos\theta = \dfrac{5^2 + 8^2 - 7^2}{2(5)(8)}$ 1M

   $= \dfrac{1}{2}$, so $\theta = 60°$ 1A

   (b) Area $= \dfrac{1}{2}(5)(8)\sin 60°$ 1M

   $= 10\sqrt{3}$ cm² 1A