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Trigonometry Main topics:

1. General Angles a. General Angles b. Basic Angles

2. Trigonometric Ratios of any angles a. 4 Quadrants b. Negative Angles c. Complementary Angles d. Special Angles

3. Solving Trigo Equations 4. Trigo Graphs

a. Basic Shapes b. Amplitude, Period & Line of Equilibrium (effect of a, b and c)

5. Identities 6. Further Identities

a. Compound Angle b. Double Angle / Half-Angle c. R Formula d. Factor Formula (sum-to-product and product-to-sum)

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General Angles

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Basic Angles

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Example

Example

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Solving Trigo Equations

Example

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Trigo Graphs Basic Trigo Graphs

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Amplitude, Period & Line of Equilibrium

cbxay += sin and cbxay += cos a: determines the amplitude

b: determines the period (i.e., bπ2 rad. Or

b

o360)

c: line of equilibrium (‘the middle line’) Example

Amplitude

Amplitude

Period

Axis of the Curve

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Summary of Trigo Graphs

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Trigonometric Identities

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Example

Example

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Further Trigonometric Identities

Example

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Example

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Double Angle Formula

Half Angle Formula

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Example

Example

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R Formula

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Example

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Factor Formula (Sum-to-product, Product-to-sum)

Example