Section 3.5 Cosecant Secant and Cotangent Functions © Copyright all rights reserved to Homework depot: www.BCMath.ca

i) Review: Reciprocal Functions The reciprocal function takes the reciprocal of all the y-coordinates of a function When graphing a reciprocal function, there are a three main steps: The reciprocal of 1 or -1 will be the same, so points with a y-coordinate of 1 will not change The reciprocal of zero is undefined, so points with a y-coordinate of zero will become a vertical asymptote Take the reciprocal of all y-coordinates to find where the points of the new function is. Reciprocal of large numbers become small Reciprocal of small numbers become large © Copyright All Rights Reserved Homework Depot www.BCMath.ca

Practice: Given the following Function, graph the reciprocal x y -5 5 Find the x-intercept  Vertical Asymptote Find common points with a Y-coordinate of 1 or -1 Pick some points on the original Function and take the reciprocal of the Y-coordinate Reciprocal of large numbers will become small Reciprocal of small numbers Will become large © Copyright All Rights Reserved Homework Depot www.BCMath.ca

II) Reciprocal of Trigonometric Functions Cosecant is the reciprocal of the sine function Secant is the reciprocal of the cosine function Cotangent is the reciprocal of the tangent function © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Determine the value of each expression to 3 decimal places

III) Graphing Cosecant Function x y p 2p 3p 4p 5p -2 2 When sinθ=0 , you will get Vertical Asymptotes When sinθ=1 or -1, you will get Common points Take the reciprocal of each sub-domain Y-coordinates are large  Reciprocal will be small Y-coordinates are small  Reciprocal will be large © Copyright all rights reserved to Homework depot: www.BCMath.ca

IV) Graphing Secant Function x y p 2p 3p 4p 5p -2 2 When cosθ=0 , you will get Vertical Asymptotes When cosθ=1 or -1, you will get Common points Take the reciprocal of each sub-domain Y-coordinates are large  Reciprocal will be small Y-coordinates are small  Reciprocal will be large © Copyright all rights reserved to Homework depot: www.BCMath.ca

V) Graphing Cotangent Function x y p 2p 3p 4p 5p -2 2 V.A. from tanθ will become x-intercepts When tanθ=0 , you will get Vertical Asymptotes When tanθ=1 or -1, you will get Common points Y-coordinates are large  Reciprocal will be small Y-coordinates are small  Reciprocal will be large © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Indicate the Domain & Range for each of the following functions: y p 2p 3p 4p -2 2 x y p 2p 3p 4p -2 2 x y p 2p 3p 4p -2 2

Ex: Solve for θ in each of the following: Take the reciprocal of both sides Take the reciprocal of both sides The ratio is positive The ratio is negative

Homework: Assignment 3.5