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Topics · Trigonometry (2-D)

Trigonometry in DSE Maths Paper 2

Trigonometry in Paper 2 is about angles and lengths in plane figures, and about trigonometric expressions in their own right. Questions ask you to express a length or a ratio through sine, cosine and tangent, simplify with the basic identities, and solve trigonometric equations over a given interval.

What this topic covers

  • Sine, cosine and tangent in right-angled triangles
  • Simplifying with sin²θ + cos²θ = 1 and tan θ = sin θ / cos θ
  • Solving trigonometric equations for 0° ≤ θ ≤ 360°
  • Graphs of the trigonometric functions

Two sample questions

Sample 1

QPR is a straight line and S is a point such that PS QR. If angle PQS equals 35 degrees and angle PRS equals alpha, then PQ over PR equals

  1. Atangent 35 degrees over tangent alpha .
  2. Bcosine alpha over cosine 35 degrees .
  3. Ctangent alpha over tangent 35 degrees .
  4. Dcosine 35 degrees over cosine alpha .
Show the answer and solution

Answer: C

Worked solution

tan⁡35∘\displaystyle \tan 35^\circ=PSPQ\displaystyle {}= \dfrac{PS}{PQ}⇒PQ\displaystyle {}\Rightarrow PQ=PStan⁡35∘\displaystyle {}= \dfrac{PS}{\tan 35^\circ}tan⁡α\displaystyle \tan \alpha=PSPR\displaystyle {}= \dfrac{PS}{PR}⇒PR\displaystyle {}\Rightarrow PR=PStan⁡α\displaystyle {}= \dfrac{PS}{\tan \alpha}PQPR\displaystyle \dfrac{PQ}{PR}=tan⁡αtan⁡35∘\displaystyle {}= \dfrac{\tan \alpha}{\tan 35^\circ}

Sample 2

For 0 degrees less than or equal to theta less than or equal to 360 degrees, find the difference between the greatest root and the least root of the equation 10 cosine squared theta plus 21 sine theta equals 19, correct to the nearest degree.

  1. A106 degrees
  2. B137 degrees
  3. C143 degrees
  4. D286 degrees
Show the answer and solution

Answer: A

Worked solution

10(1−sin⁡2θ)+21sin⁡θ=19\displaystyle 10(1 - \sin^2 \theta) + 21\sin \theta = 1910sin⁡2θ\displaystyle 10\sin^2 \theta−21sin⁡θ\displaystyle {}- 21\sin \theta+9\displaystyle {}+ 9=0\displaystyle {}= 0⇒(5sin⁡θ−3)(2sin⁡θ−3)\displaystyle {}\Rightarrow (5\sin \theta - 3)(2\sin \theta - 3)=0\displaystyle {}= 0sin⁡θ=35\displaystyle \sin \theta = \frac{3}{5} or sin⁡θ=32\displaystyle \sin \theta = \frac{3}{2} (rejected)θ≈36.87∘,143.13∘\displaystyle \theta \approx 36.87^\circ, 143.13^\circgreatest root−\displaystyle -{}least root≈143.13∘\displaystyle {}\approx 143.13^\circ−36.87∘\displaystyle {}- 36.87^\circ=106.26∘\displaystyle {}= 106.26^\circ∴\displaystyle \therefore the required difference≈106∘\displaystyle \approx 106^\circ (correct to the nearest degree)

Try a whole paper

The free mock is a full 45-question Paper 2 under exam timing, marked the moment you submit, with a report by topic.

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Original material by Dsetopia, written from the EDB syllabus learning objectives. Not affiliated with the HKEAA; no exam content is reproduced.