Trigonometry |
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Trigonometric Ratios |
1. Trigonometric ratios for 30°, 45° and 60° |
2. Trig ratios for multiples of 30°, 45° and 60° |
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Trigonometric Graphs and Transformations |
1. Trigonometric graphs |
2. Translations of trig graphs |
3. Reflections of trig graphs |
4. Stretches of trig graphs |
5. Combining transformations |
6. Exam Questions - Trigonometric graphs and transformations |
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Applications of Trigonometry – Playlist |
1. Area of a triangle - Given two sides and an included angle |
2. Sine rule |
3. Exam Questions - Sine rule |
4. Cosine rule |
5. Radians |
6. Arcs, sectors and segments |
7. Exam Questions - Arcs, sectors and segments |
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Trigonometric Equations – Playlist |
1. Quadrant rule to solve trig equations |
2. Trig equations with different ranges |
3. Trig equations with multiple angles |
4. Trig equations that factorise |
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Trigonometric Identities – Playlist |
1. Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1 |
2. Using the identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ) |
3. Solving equations using identities |
4. Exam Questions - Trigonometric identities |
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Sec θ, Cosec θ and Cot θ – Playlist |
1. Trig functions sec θ, cosec θ and cot θ |
2. Graphs of sec θ, cosec θ and cot θ |
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Inverse trigonometric functions – Playlist |
1. Inverse trigonometric functions - arcsin x, arccos x, arctan x |
2. Examples using Inverse trigonometric functions |
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Identities & Equations – Pythagorean Type – Playlist |
1. sin²x + cos²x ≡1 , 1 + tan²x ≡ sec²x , 1 + cot²x ≡ cosec²x |
2. Examples using Pythagorean identities |
3. Solving equations using Pythagorean identities |
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Small-angle Approximations – Playlist |
1. Small-angle approximations |
2. Exam Questions - Small Angle Approximations |
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Identities – Addition type – Playlist |
1. sin(A±B), cos(A±B) and tan(A±B) |
2. Using the Addition formulae to get exact values |
3. Proving identities using the addition formulae |
4. Identities - Addition type - Equations |
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Identities & Equations – Double angle type – Playlist |
1. Identities for sin2A, cos2A and tan2A |
2. Examples using double angle identities |
3. Solving equations using double angle identities |
4. Exam Questions - Double Angles |
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Identities – Half angle type – Playlist |
1. Examples using half angle identities |
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Identities – Triple angle type – Playlist |
1. Identity for cos 3θ and sin 3θ |
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Identities & Equations – Harmonic Formulae – Playlist |
1. Harmonic Identities Rsin(x ± α), Rcos(x ± α) |
2. Equations using harmonic identities |
3. Harmonic identities - Max and Min |
4. Exam Questions - Harmonic identities and equations |
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Exam Questions – Mixed trigonometry |
1. Exam Questions - Mixed trigonometry |