Trigonometric Functions practice questions

Secondary 3 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise trigonometric functions free

What this topic covers

Worked examples

Example 1

Without a calculator, find the exact value of 8sin⁡30∘×cos⁡30∘×tan⁡60∘8\sin 30^\circ \times \cos 30^\circ \times \tan 60^\circ.
Show the worked solution
  • $8 \times \frac{1}{2} \times \frac{\sqrt{3}}{2} \times \sqrt{3} = 8 \times \frac{3}{4} = 6$.

Answer: 66

Example 2

Given that sin⁡θ=−725\sin \theta = -\frac{7}{25} and θ\theta is in the 3rd quadrant, find cos⁡θ\cos \theta.
Show the worked solution
  • $\theta$ is in Q3. Using ASTC: sin is −, cos is −, tan is +.
  • Using the Pythagorean triple $(7, 24, 25)$:
  • $\cos \theta = -\frac{24}{25}$

Answer: −24/25-24/25

Example 3

Find the period (in degrees) of y=5cos⁡ 3xy = 5\cos\, 3x.
Show the worked solution
  • Period $= \frac{360^\circ}{b}$.
  • Period $= \frac{360^\circ}{3}$.
  • Period $= 120^\circ$.

Answer: 120120

Questions parents ask

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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