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Trigonometric Functions

Secondary 3 Additional Math practice

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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 24sin⁡230∘×cos⁡245∘24\sin^2 30^\circ \times \cos^2 45^\circ.
Show the worked solution
  • 24×14×12=24×1824 \times \frac{1}{4} \times \frac{1}{2} = 24 \times \frac{1}{8}
  • =3= 3

Answer: 33

Example 2

Given that sin⁡θ=−35\sin \theta = -\frac{3}{5} and θ\theta is in the 4th quadrant, find tan⁡θ\tan \theta.
Show the worked solution
  • θ\theta is in Q4. Using ASTC: sin is −, cos is +, tan is −.
  • For the basic angle, the opposite side is 33 and the hypotenuse is 55.
  • adjacent=52−32Pythagoras\text{adjacent} = \sqrt{5^2 - 3^2} \quad \scriptsize\textit{Pythagoras}
  • =16= \sqrt{16}
  • =4= 4
  • tan⁡θ=−34\tan \theta = -\frac{3}{4}

Answer: −3/4-3/4

Example 3

Find the period (in degrees) of y=2sin⁡ 6x+2y = 2\sin\, 6x + 2.
Show the worked solution
  • Period =360∘b= \frac{360^\circ}{b}.
  • Period =360∘6= \frac{360^\circ}{6}.
  • Period =60∘= 60^\circ.

Answer: 6060

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

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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