Master Year 12 Trigonometry

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Trigonometry Topics

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1. Right Triangle Trigonometry

1.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

1.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

1.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

1.4

Combination of SohCahToa questions

1.5

Solving expressions using 45-45-90 special right triangles

1.6

Solving expressions using 30-60-90 special right triangles

1.7

Word problems relating ladder in trigonometry

1.8

Word problems relating guy wire in trigonometry

1.9

Other word problems relating angles in trigonometry

2. Trigonometric Ratios and Angle Measure

2.1

Angle in standard position

2.2

Coterminal angles

2.3

Reference angle

2.4

Find the exact value of trigonometric ratios

2.5

ASTC rule in trigonometry (All Students Take Calculus)

2.6

Unit circle

2.7

Converting between degrees and radians

2.8

Trigonometric ratios of angles in radians

2.9

Radian measure and arc length

2.10

Law of sines

2.11

Law of cosines

2.12

Applications of the sine law and cosine law

3. Bearings

3.1

Introduction to bearings

3.2

Bearings and direction word problems

3.3

Angle of elevation and depression

4. Graphing Trigonometric Functions

4.1

Sine graph: y = sin x

4.2

Cosine graph: y = cos x

4.3

Tangent graph: y = tan x

4.4

Cotangent graph: y = cot x

4.5

Secant graph: y = sec x

4.6

Cosecant graph: y = csc x

4.7

Graphing transformations of trigonometric functions

4.8

Determining trigonometric functions given their graphs

5. Applications of Trigonometric Functions

5.1

Ferris wheel trig problems

5.2

Tides and water depth trig problems

5.3

Spring (simple harmonic motion) trig problems

6. Trigonometric Identities

6.1

Quotient identities and reciprocal identities

6.2

Pythagorean identities

6.3

Sum and difference identities

6.4

Cofunction identities

6.5

Double-angle identities

7. Solving Trigonometric Equations

7.1

Solving first degree trigonometric equations

7.2

Determining non-permissible values for trig expressions

7.3

Solving second degree trigonometric equations

7.4

Solving trigonometric equations involving multiple angles

7.5

Solving trigonometric equations using pythagorean identities

7.6

Solving trigonometric equations using sum and difference identities

7.7

Solving trigonometric equations using double-angle identities

8. Inverse Trigonometric Functions

8.1

Finding inverse trigonometric function from its graph

8.2

Evaluating inverse trigonometric functions

8.3

Finding inverse reciprocal trigonometric function from its graph

8.4

Finding exact value of inverse reciprocal trig functions

9. Imaginary and Complex Numbers

9.1

Introduction to imaginary numbers

9.2

Complex numbers and complex planes

9.3

Adding and subtracting complex numbers

9.4

Complex conjugates

9.5

Multiplying and dividing complex numbers

9.6

Distance and midpoint of complex numbers

9.7

Angle and absolute value of complex numbers

9.8

Polar form of complex numbers

9.9

Operations on complex numbers in polar form

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