Mathematics

Trigonometrical Functions

Posted by Asok K Nadhani on

Last Updated on: 15th February 2024, 12:58 pm

Trigonometrical Functions

In a Right-Angled Triangle, where A= 𝜃 is the acute angle, the hypotenuse h is the side that connects the two acute angles. The side b adjacent to 𝜃 (also referred as Base of the triangle here) is the side of the triangle that connects 𝜃 to the right angle. The third side a is said to be opposite to 𝜃 (also referred as Perpendicular of the triangle here).

If the angle 𝜃 is given, then all sides of the right-angled triangle may be defined in terms of the Angle 𝜃. This means that the ratio of any two side lengths depends only on 𝜃. Thus, we may define six functions of 𝜃, which are the Trigonometric Functions.

Trigonometrical Functions

Sin \displaystyle \theta = Opposite or Perpendicular (BC)/Hypotenuse (AB)=\displaystyle \frac{a}{h}. Cosec \displaystyle \theta =\displaystyle \frac{h}{a}=1/Sin\displaystyle \theta

Cos \displaystyle \theta = Base or Adjacent (AC)/Hypotenuse (AB)=\displaystyle \frac{b}{h}. Sec \displaystyle \theta =\displaystyle \frac{h}{b}=1/Cos\displaystyle \theta

Tan \displaystyle \theta = Perpendicular or Opposite(BC)/Base or Adjacent (AC)=\displaystyle \frac{a}{b}. Cot \displaystyle \theta =\displaystyle \frac{b}{a}=1/Tan\displaystyle \theta