Trigonometry
Trigonometry for IB Analysis and Approaches HL: radians, ratios, identities, trigonometric equations, sine and cosine rules, with IB exam questions.
Trigonometry relates the angles of a triangle to the lengths of its sides. It starts with the right-angled triangle, extends to any angle with the unit circle and radians, and ends by solving any triangle with the sine and cosine rules. Along the way come the identities (addition and double angle) and the trigonometric equations, which the IB asks about in almost every exam session.
Recommended order
Follow the sections in order: each one uses what came before. If you already know the right-angled triangle well, start with the radians and the unit circle. At the end you will find the IB exam questions grouped by type.
Quadratic equations (topic 1) and Pythagoras' theorem.
Sections in this topic
Trigonometric ratios in right-angled triangles
Sine, cosine and tangent, basic identities, exact values of 30°, 45° and 60°, and how to solve right-angled triangles, for IB Analysis and Approaches HL.
3 worked examples Section 2Radians and the unit circle
Radians, arc length, sector area, trigonometric ratios of any angle, quadrant signs, and sec, cosec and cot, for IB Analysis and Approaches HL.
3 worked examples Section 3Sum, double-angle and half-angle identities
Sum, double-angle and half-angle formulas for sine, cosine and tangent, exact values and how to prove identities, for IB Analysis and Approaches HL.
3 worked examples Section 4Trigonometric equations
How to solve sine, cosine and tangent equations over an interval, including kx, quadratic and double-angle equations, for IB Analysis and Approaches HL.
3 worked examples Section 5Sine and cosine rules; area of a triangle
Sine and cosine rules, the ambiguous case, area ½ab sin C, bearings and angles of elevation and depression, with worked examples for IB AA HL.
3 worked examples End of topicIB exam questions: topic 4
IB exam questions on trigonometry: radians, identities, equations and the sine and cosine rules (Analysis and Approaches HL), with worked solutions.
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