Mathematics Dictionary

Text and examples Trigonometric functions in various quadrants
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- 1. Prove that sin(90-A) = cos(A) and sin(90+A) = cos(A).
- 2. Prove that sin(180-A) = sin(A) and sin(180+A) = -sin(A).

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TR 05. Relations between functions

Text and examples Relation between functions
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- 1. Pythagorean relations.
- 2. Unit circle and unit hyperbola.
- 3. Parametric equations.

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TR 06. Graphs of trigonopmetric functions

Text and examples Graphs of trigonopmetric functions
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- 1. The sine curve and its period.
- 2. The tangent curve and its period.
- 3. The secant curve and its period.

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TR 07. Functions of compound angles

Text and examples Functions of compound angles
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- 1. Sum angles : sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B).
- 2. Different angles : sin(A-B) = sin(A)*cos(B) - cos(A)*sin(B).
- 3. Multiple angles.

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TR 08. Inverse trigonometric functions

Text and examples Inverse trigonometric functions
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- 1. Properties of inverse function.

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TR 09. Trigonometric equations

Text and examples Trigonometric equations
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- 1. General solution of sin(x) = a.
- 2. General solution of cos(x) = a.
- 2. General solution of tan(x) = a.

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TR 10. Angles and sides of triangle

Text and examples Angles and sides of triangle
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- 1. Sine law.
- 2. Cosine law = a.
- 3. Sin(A) = Sqr(s*(s-a)*(s-b)*(s-c))/(2*b*c).

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TR 11. Identities in Trigonometry

Text and examples Angles and sides of triangle
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- 1. Prove sin(2*A)+sin(2*B)+sin(2*C) = 4*sin(A)*sin(B)*sin(C) if A+B+C = 180°.
- 2. Prove tan(A)+tan(B)+tan(C) = tan(A)*tan(B)*tan(C) if A+B+C = pi.

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TR 12. DeMoivre's theory

Text and examples Angles and sides of triangle
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- 1. cis(A)^n = cis(n*A) if n is integers
- 2. cis(A)^(1/n) = cis((2*k*pi+A)/n) where k = 0, 1, 2, ..... (n-1).

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TR 13. Trigonometric series

Text and examples Series
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- 1. sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ......
- 2. cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ......

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TR 14. Special topics

Text and examples Special topics
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- 1. S.H.M.
- 2. Projectiles.
- 3. Lim[sin(x)/x] = 1.
- 4. Find sin(18) and cos(18).

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TR 15. Functions in polar coordinates

Text and examples Functions in polar coordinates
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- 1. Graphs of R = a + b*F(p*A/q)^M
- 2. Graphs of R = 1 + 1*sin(11*A/4)^3

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TR 16. Parametric equation

Text and examples Index
Highlight : Find graphs
- 1. What is the graph of x = sec(t) and y = tan(t) ?
- 2. What is the graph of x = tan(t) and y = sec(t) ?
- 3. What are the difference between above two graphs ?

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TR 17. Parametric equation

Text and examples New
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- circle : x = cos(t) and y = sin(t)
- Hyperbola : x = sec(t) and y = tan(t)

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TR 18. Trnasformation

Text and examples Trnasformation
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- Transform y = sin(x) to y - k = a*sin(k*x + h)
- Transform y = cos(x) to y - k = a*cos(k*x + h)

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TR 19. Examples

Text and examples Examples
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TR 20. Trigonometry Index

Text and examples Index
Highlight : Find keywords in alphabetic order
- Find keyword by two numbers
- First number is section number.
- Second number is topic number.
How to find keyword ?
- Find the section number and topic number of keyword
- 1st number : Section number
- 2nd number : Topic number
- Remeber these two numbers
- Click Back to back subject page
- Click "Goto Begin" to top
- Click section number to enter the required section
- Click topic number

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TR 21. Diagrams in Trigonometry

Subject | Trigonometry Index
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TR 22. Glossry

Subject | Glossary
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TR 23. Home work in general

Subject | Home work by keyword
Tips
- Find home work number
- On top of this page, open the web-page including this number
- Example : S31 in page S21-40

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TR 24. References

Subject | References
Highlight :
- 1. Mathematics on Internet
- 2. Mathematics on PC Computer

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TR 25. Example

Subject | Examples by keyword
Tips
- Open the example page
- Find the question by keywords and remember the the number
- Return this page and go to begin
- Open the section number
- Example : Question numbe is 07 18, then open section 08 and select topic 18

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TR 26. Formula

Subject | Formula
Tip
- Formula in computer language symbols
- Read the symbol page and then convert it to math language
- Example 1 : x^2 is square of x. Change it as x²
- Example 2 : sin(A)^2 is sin²(A)

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TR 27. Examples with solutions (QA)

Topic | Formulae in geometry

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Q00. Tips

Index and examples

Lesson 20 : Index
Lesson 21 : Application graphic programs
Lesson 22 : Glossary
Lesson 23 : Goto home works
Lesson 24 : References
Lesson 25 : Examples link to section numbers, e.g. 03 02
Lesson 26 : Formulae in trigonometry
Lesson 27 : Select examples with solution (QA)

Highlight tops (Update later)

1. Half angle formula in terms of s in Lesson 10
2. Area of triangle interms of s in TR 10 06
3. Identities in Lesson 11

Run Application graphic program (See Lesson 21)

Step 1 : Run at current location (no download)
Step 2 : Select Yes to run
Notes
- 1. The application program is only for internet use (Update monthly)
- 2. Download only available upto end of the month

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