Trigonometric Equations and Identities 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 equations and identities free

What this topic covers

Worked examples

Example 1

Solve 8tan⁡x=08\tan x = 0 for 0∘≤x≤360∘0^\circ \leq x \leq 360^\circ.
Show the worked solution
  • $\tan x = 0$
  • $\text{Basic angle} = \tan^{-1}\left(0\right) = 0^\circ$
  • $\text{tan is positive in Q1 and Q3}$
  • $x = 0^\circ \text{ or } x = 180^\circ + 0^\circ = 180^\circ$
  • $x = 0^\circ, 180^\circ, 360^\circ$

Answer: 0,180,3600,180,360

Example 2

Given cos⁡A=8089\cos A = \frac{80}{89} and AA is acute, evaluate cot⁡2A\cot^2 A.
Show the worked solution
  • $\cos A = \frac{80}{89}$
  • $\sin A = \frac{39}{89} \quad \scriptsize\textit{Pythagorean identity}$
  • $\cot A = \frac{\cos A}{\sin A}$
  • $= \frac{80}{39}$
  • $\cot^2 A = \frac{6400}{1521}$

Answer: 6400/15216400/1521

Example 3

Given that AA and BB are acute angles, sin⁡A=3989\sin A = \frac{39}{89} and cos⁡B=5573\cos B = \frac{55}{73}, find sin⁡(A−B)\sin(A - B).
Show the worked solution
  • $\sin A = \frac{39}{89} \Rightarrow \cos A = \frac{80}{89} \quad \scriptsize\textit{Pythagorean identity}$
  • $\cos B = \frac{55}{73} \Rightarrow \sin B = \frac{48}{73} \quad \scriptsize\textit{Pythagorean identity}$
  • $\sin(A - B) = \sin A \cos B - \cos A \sin B$
  • $= -\frac{1695}{6497}$

Answer: −1695/6497-1695/6497

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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