Trigonometry — IGCSE Mathematics - Additional (0606) questions by topic
Trigonometry questions ask you to solve equations involving secant and cosecant within a given angle range, show that an expression involving cosecant and tangent simplifies to secant, write down the period of a transformed tangent function, and solve an equation built from cosine-squared and sine terms within a restricted domain in radians. Find, show, state, draw and solve are the top command words, with solve tasks requiring every valid solution within the stated range, not just one.
This page holds 5 real questions worth between 4 and 10 marks, all from 2025 papers. Because missing a valid solution within a given range is a common way marks are lost, submit your worked solutions for instant marking to check you have found every root the range allows, not only the first one you spot.
May–June 2025, Paper 11
Given that 0 ≤ θ < π/2, show that sin θ / sqrt(cosec^2 θ − 1) + 1 / sqrt(1 + tan^2 θ) can be written as sec θ.
Answer this question and get it marked →May–June 2025, Paper 21
Solve the equation (2 − 3 cot x) cos x = 0 for 0 < x ⩽ π/2.
Answer this question and get it marked →May–June 2025, Paper 22
Solve the equation 3 sec 3x = sqrt(3) cosec 3x for -120 degrees <= x <= 120 degrees.
Answer this question and get it marked →May–June 2025, Paper 23
In this question, all angles are in radians. Write down the period of 5 tan(x/4) + 1.
Answer this question and get it marked →The function f is defined by f(x) = 15 cos^2(3x + 1.5) + 7 sin(3x + 1.5) − 13 for −0.3 ≤ x ≤ 0.5, where x is in radians. Solve the equation f(x) = 0.
Answer this question and get it marked →