An introduction to Trigonometry

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Contents: 

# Definitions and basics 

* Trigonometric circle and angles 
* Trigonometric numbers of a real number t 
* Basic formulas 
* Related values 
* supplementary values 
* complementary values 
* Opposite values 
* Anti supplementary values 
* The right-angled triangle 
* Area of a triangle 
* Sine rule 
o Homogeneous expression in a, b and c 
* Cosine rule 

# Trigonometric functions 

* The sine function 
* The cosine function 
* The tangent function 
* The cotangent function 

# Inverse Trigonometric Functions 

* The arcsin function 
* The arccos function 
* The arctan function 
* The arccot function 

# Sum formulas 

* cos(u - v) 
* cos(u + v) 
* sin(u - v) 
* sin(u + v) 
* tan(u + v) 
* tan(u - v) 
* sin(2u) 
* cos(2u) 
* tan(2u) 
* Carnot formulas 
* t-formulas 

# Special values 

* pi/3 
* pi/4 
* pi/6 

# Trigonometric equations 

* Base equations 
o cos(u) = cos(v) 
o sin(u) = sin(v) 
o tan(u) = tan(v) 
o cot(u) = cot(v) 
* Reducing to base equations 
* Using an additional unknown 
* Using factorization 
* The equation a.sin(u)+b.cos(u) = c 
* Homogeneous equations 

# Calculations with inverse trigonometric functions