EduNinja

A-Level CAIE Mathematics A23.3 TrigonometryQuestion Bank

[Maximum number: 3]

Prove the identity cot⁡x−tan⁡xcot⁡x+tan⁡x≡cos⁡2x\frac{\cot x-\tan x}{\cot x+\tan x} \equiv \cos 2 x.

[Maximum number: 5]

Solve the equation cos⁡(θ−60∘)=3sin⁡θ\cos \left(\theta-60^{\circ}\right)=3 \sin \theta, for 0∘⩽θ⩽360∘0^{\circ} \leqslant \theta \leqslant 360^{\circ}.

[Maximum number: 5]

Showing all necessary working, solve the equation cot⁡θ+cot⁡(θ+45∘)=2\cot \theta+\cot \left(\theta+45^{\circ}\right)=2, for 0∘<θ<180∘0^{\circ}<\theta<180^{\circ}.

[Maximum number: 5]

Solve the equation 5tan⁡2θ=4cot⁡θ5 \tan 2 \theta=4 \cot \theta for 0∘<θ<180∘0^{\circ}<\theta<180^{\circ}.

(a)

Given that tan⁡2θcot⁡θ=8\tan 2 \theta \cot \theta=8, show that tan⁡2θ=34\tan ^{2} \theta=\frac{3}{4}.

[ 3 ]
(a)

Express 24sin⁡θ−7cos⁡θ24 \sin \theta-7 \cos \theta in the form Rsin⁡(θ−α)R \sin (\theta-\alpha), where R>0 and 0∘<α<90∘0^{\circ}<\alpha<90^{\circ}. Give the value of α\alpha correct to 2 decimal places.

[ 3 ]
(b)

Hence find the smallest positive value of θ\theta satisfying the equation

24sin⁡θ−7cos⁡θ=1724 \sin \theta-7 \cos \theta=17
[Maximum number: 5]

Express the equation sec⁡θ=3cos⁡θ+tan⁡θ\sec \theta=3 \cos \theta+\tan \theta as a quadratic equation in sin⁡θ\sin \theta. Hence solve this equation for −90∘<θ<90∘-90^{\circ}<\theta<90^{\circ}.

[Maximum number: 6]

By first expressing the equation tan⁡(x+45∘)=2cot⁡x+1\tan \left(x+45^{\circ}\right)=2 \cot x+1 as a quadratic equation in tan⁡x\tan x, solve the equation for 0∘<x<180∘0^{\circ}<x<180^{\circ}.

[Maximum number: 5]

Showing all necessary working, solve the equation cot⁡2θ=2tan⁡θ\cot 2 \theta=2 \tan \theta for 0∘<θ<180∘0^{\circ}<\theta<180^{\circ}.

(a)

Show that 12sin⁡2xcos⁡2x≡32(1−cos⁡4x)12 \sin ^{2} x \cos ^{2} x \equiv \frac{3}{2}(1-\cos 4 x).

[ 3 ]
0 selected