(ebook) [math] Trigonometry

# (ebook) [math] Trigonometry - Maths Extension 1...

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Maths Extension 1 – Trigonometry Trigonometry Trigonometric Ratios Exact Values & Triangles Trigonometric Identities ASTC Rule Trigonometric Graphs Sine & Cosine Rules Area of a Triangle Trigonometric Equations Sums and Differences of angles Double Angles Triple Angles Half Angles T – formula Subsidiary Angle formula General Solutions of Trigonometric Equations Radians Arcs, Sectors, Segments Trigonometric Limits Differentiation of Trigonometric Functions Integration of Trigonometric Functions Integration of sin 2 x and cos 2 x INVERSE TRIGNOMETRY Inverse Sin – Graph, Domain, Range, Properties Inverse Cos – Graph, Domain, Range, Properties Inverse Tan – Graph, Domain, Range, Properties Differentiation of Inverse Trigonometric Functions Integration of Inverse Trigonometric Functions http://fatmuscle.cjb.net 1

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Maths Extension 1 – Trigonometry Trigonometric Ratios Sine sin θ = hypotenuse opposite Cosine cos θ = hypotenuse adjacent Tangent tan θ = adjacent opposite Cosecant cosec θ = θ sin 1 = opposite hypotenuse Secant sec θ = θ cos 1 = adjacent hypotenuse Cotangent cot θ = θ tan 1 = opposite adjacent sin θ = ( 29 θ - ° 90 cos cos θ = ( 29 θ - ° 90 sin tan θ = ( 29 θ - ° 90 cot cosec θ = ( 29 θ - ° 90 sec sec θ = ( 29 θ - ° 90 cos ec cot θ = ( 29 θ - ° 90 tan 60 seconds = 1 minute 60’’ = 1’ 60 minutes = 1 degree 60’ = 1° θ θ θ cos sin tan = θ θ θ sin cos cot = http://fatmuscle.cjb.net 2 θ θ hypotenuse hypotenuse opposite adjacent adjacent opposite
Maths Extension 1 – Trigonometry Exact Values & Triangles 30° 60° 45° 90° 180° sin 0 2 1 2 3 2 1 1 0 cos 1 2 3 2 1 2 1 0 –1 tan 0 3 1 3 1 –– 0 cos ec –– 2 3 2 2 1 –– sec 1 3 2 2 2 –– –1 cot –– 3 3 1 1 0 –– Trigonometric Identities θ θ 2 2 cos sin + = 1 θ 2 cos = θ 2 sin 1 - θ 2 sin = θ 2 cos 1 - θ 2 cot 1 + = cosec 2 θ θ 2 cot = cosec 2 θ – 1 1 = cosec 2 θ θ 2 cot 1 tan 2 + θ = θ 2 sec θ 2 tan = 1 sec 2 - θ 1 = θ θ 2 2 tan sec - http://fatmuscle.cjb.net 3 1 1 2 45° 3 1 2 30° 60°

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Maths Extension 1 – Trigonometry ASTC Rule First Quadrant: A ll positive θ sin θ sin + θ cos θ cos + θ tan θ tan + Second Quadrant: S ine positive ( 29 θ - ° 180 sin θ sin + ( 29 θ - ° 180 cos θ cos ( 29 θ - ° 180 tan θ tan Third Quadrant: T angent positive ( 29 θ + ° 180 sin θ sin ( 29 θ + ° 180 cos θ cos ( 29 θ + ° 180 tan θ tan + Fourth Quadrant: C osine positive ( 29 θ - ° 360 sin θ sin ( 29 θ - ° 360
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