Basics Of Trigonometry

 Basics Of Trigonometry
Trigonometric Ratios of Particular Angles: 
In the above picture if triangle is drawn for an angle  for which ever side lenghts we get always Hypotenuse length is twice to perpendicular length. It means   
    \(\frac{{Perpendicular}}{{Hypotenuse}} = \frac{{MP}}{{OP}} = \frac{a}{c} = \frac{1}{2} = \sin {30^0} = {\text{constant}}\)
It says if a=1 unit, then c=2 units. By using Pythagorean theorem 
 c²=a²+b², we get b=\(\sqrt{3}\)
     Therefore 
\(\cos {30^0} = \frac{b}{c} = \frac{{\sqrt 3 }}{2},\tan {30^0} = \frac{a}{b} = \frac{1}{{\sqrt 3 }},\cot {30^0} = \frac{b}{a} = \sqrt 3 ,\sec {30^0} = \frac{c}{b} = \frac{2}{{\sqrt 3 }},\cos ec{30^0} = \frac{c}{a} = 2\)
similarly if we verify these ratios always constant for different angles, independent of side length of right angled triangle.