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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
2 Radians and degrees
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
4 Solving trigonometric quadratic equations
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
5 Navigation problems
IX MISCELLANEOUS TOPICS
A. Complex numbers
1 Meaning
2 Operations
a) Addition and subtraction
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
1 Addition
2 Multiplication
3 Other operations
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