TRIGONOMETRY
Areas of focus:
One revolution is 360^{o}, and is also 2 radians. Thus, due to linear proportionality of the two scales, the conversion from x degrees to y radians is:
One radian is equal to 3.14159..., and is normally approximated by 3.14. The following table gives equivalent angles in degrees, radians, and revolutions.
Degrees 
Radians 
Revolutions 
0^{o} 
0 
0 
30^{o} 


45^{o} 


60^{o} 


90^{o} 


180^{o} 


270^{o} 


360^{o} 

1 
The trigonometric functions are named sine, cosine, tangent, cotangent, secant, and cosecant. A trigonometric function has one argument that is an angle and will be denoted "". In writing the trigonometric functions one uses the abbreviated forms: , , , , , and , respectively. Also, sometimes these are written as , , , , , and , respectively.
The value of each trigonometric function for an acute angle (<90^{o}) can be directly related to the sides of a right triangle. Consider the angle in the following figure. The values of the trigonometric functions for this angle are given as:
Note: the exponents of trigonometric functions follow a special rule. If the exponent "n" is positive, then one writes in place of . For example,
The same rule does not apply to negative exponents since the exponent "1" is reserved for the inverse trigonometric function.
Functions of Complementary Angles:
In this figure, and are complementary angles, meaning . Examination of the basic relation between the trigonometric functions and the sides of the triangle reveal the following relations between the complementary angles and.
Since , we can also write:
The Pythagorean theorem states that for a right triangle, as shown, there exists a relation between the length of the sides given be
a^{2} + b^{2} = c^{2}
There are also Pythagorean triples for (a,b,c), such as (3,4,5), (5,12,13) and (7,24,25) sided triangles, and all constant multiples of these triplets (e.g., (6,8,10)).
Fundamental Relations Among Trigonometric Functions:
From the Pythagorean Theorem of plane geometry we know that x^{2} + y^{2} = r^{2}. This can be used to derive a basic relation between the sine and cosine functions.