Math

Trigonometric Ratios and Pythagorean Theorem

 

1) Sine of an angle: In a right triangle, the sine or sin of an angle is the ratio of the side opposite to the angle to the hypotenuse: 

 

                                                 

 

2) The Cosine of an angle: In a right triangle, the cosine or cos of an angle is defined as the ratio of the side adjacent to an acute angle to the hypotenuse. 

 

                                               

 

3) Tangent of an angle: Tangent or Tan of an angle is defined as the ratio of the side opposite to an angle to the side adjacent to the angle.

 

                                               

 

4) Cotangent of an angle: Cotangent or Cot of an angle is defined as the ratio of the side adjacent to an angle to the side opposite to the angle.

 

                                                

 

5) Cosecant of an angle: Cosecant or Csc of an angle is defined as the ratio of the hypotenuse to the side opposite to the angle.

 

 

6) Secant of an angle: Secant or Sec of an angle is defined as the ratio of the hypotenuse to the side adjacent to the angle.

 

                                                

Example: Find the trig ratios of the given angle.

 

                                                      

 

Example: In the triangle shown below, find the value of x.

 

                                                        

Pythagorean Theorem

The Pythagorean theorem states a fundamental relationship between three sides of a right triangle. According to this theorem, the area of a square whose side is the hypotenuse  is equal to the sum of the areas of the squares whose sides are the other two sides of a right triangle.

                                            

 

Example: Find the unknown side of the triangle below.

 

                                                   

 

We use the Pythagorean theorem to find c: