iGCSE Mathematics (0580) :E6.4 Solve problems using the sine and cosine rules.iGCSE Style Questions Paper 2

Question

(a) Sketch the graph of y = tan x for 0° ≤ x ≤ 360°.

(b) Solve the equation 5tan x = 1 for 0° ≤ x ≤ 360°.

▶️ Answer/Explanation

Solution

(a) Graph with correct shape: asymptotes at 90° and 270°, passing through (0,0), (180,0), (360,0)

(b) 11.3° and 191.3°

tan x = 1/5 ⇒ x = tan⁻¹(0.2) ≈ 11.3°

Second solution: 11.3° + 180° = 191.3°

Question

Graph grid

(a) On the diagram, sketch the graph of \(y=\cos x\) for \(0^{\circ}\leq x\leq 360^{\circ}\).

(b) Solve the equation \(4\cos x+2=3\) for \(0^{\circ}\leq x\leq 360^{\circ}\).

▶️ Answer/Explanation

(a)

Cosine graph

(b) Answer: \(75.5^\circ\) and \(284.5^\circ\)

Solve \(4\cos x + 2 = 3\) → \(\cos x = 0.25\). Solutions in \(0^\circ \leq x \leq 360^\circ\) are \(75.5^\circ\) and \(284.5^\circ\) (using symmetry of cosine).

iGCSE Mathematics (0580) :E6.4 Solve problems using the sine and cosine rules.iGCSE Style Questions Paper 2

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