More Right Triangle Trig. (cosecant, secant, cotangent)

Besides the original Trig functions, there are also three more methods to use: Cosecant, Secant, Cotangent

These functions are inverses of the normal trig functions. They may be used instead of the normal functions if the appropriate angles

 or sides are present that make the inverses better choices for solving the triangle.

    Cosecant:     csc ø =  the length of the hypotenuse                 =  ___1___                                       length of the side opposite the angle            sin ø    Secant:         sec ø = the length of the hypotenuse                  =  ___1___                                      length of the side adjacent to the angle         cos ø                                               Cotangent:    cot ø = length of the side adjacent to the angle  =   ___1___                                      length of the side opposite the angle              tan øExample            A biologist wants to know the width w of a river in order to properly set instruments for studying                            the pollutants in the river. From point A, the biologist walks downstream 100 feet and sights to                                                      point C. From this sighting, it is determined that ø = 58o . How wide is the river? 

                                                                        First Step: Find out what you know to draw the triangle.

                                                                        Second Step: Find our what Trig function to use.

                                                                        Third Step: Plug the numbers into the formula

                                                                        Fourth Step: Solve for ø.

                                                                        cot ø = adjacent

                                                                                    opposite

                                                                                                                   cot 58º =   100