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VIII TRIGONOMETRY

A. Trigonometry of the right triangle

1 Definitions of the six functions

2 Relations of the functions of the complementary angles

3 Reciprocal relations among the functions

4 Variations in the functions of acute angles

5 Pythagorean and quotient relations

6 Functions of 30°, 45°, and 60°

7 Applications of the functions to right triangle problems

B. Trigonometric functions of the general angle

1 Generating an angle of any size

3 Using radians to determine arc length

4 Definitions of the functions of an angle

5 Signs of the functions in the four quadrants

6 Functions of the quadrantal angle

7 Finding the value of functions of any angle

C Identities and equations

1 Difference between identities in equations

2 Proving identities

3 Solving linear trigonometric functions

D Generalized trigonometric relationships

1 Functions of the sum of two angles

2 Functions of the difference of two angles

3 Functions of the double angle

4 Functions of the half angle

E Graphs of trigonometric functions

1 Graphs of the sine, cosine, and tangent curves

2 Properties of the sine, cosine, and tangent curves

3 Definitions of amplitude, period, and frequency

4 Solving trigonometric equations graphically

F Solutions of oblique triangles

1 Law of sines

2 Law of cosines

3 Using logarithms to solve oblique triangle problems

4 Vector problems—parallelogram of forces

IX MISCELLANEOUS TOPICS

A. Complex numbers

1 Meaning

2 Operations

b) Multiplication and division

i Powers of i

ii Complex conjugate

3 Complex roots of quadratic equations

B Number Bases

1 Converting from base 10 to other bases

2 Converting from other bases to base 10

3 Operations in other bases

C Exponents and logarithms

1 Meaning of logarithms

2 Computation with exponents and logarithms

3 Equations

4 Graphs of exponential and logarithmic functions

D Binary operations

1 Definition of binary operations

2 Properties of binary operations

3 Application to modular arithmetic

E Identity and inverse elements