Presentation on theme: "Aim: How can we graph the reciprocal trig functions using the three basic trig ones? Do Now: In the diagram below of right triangle JMT, JT = 12, JM ="— Presentation transcript:
1Aim: How can we graph the reciprocal trig functions using the three basic trig ones? Do Now:In the diagram below of right triangle JMT, JT = 12, JM = 6 and mJMT = 90. What is the value of cot J?JMT
3Trig Values in Coordinate Plane yQuadrant IIQuadrant Ifunctionreciprocalfunctionreciprocalcos is –sin is +tan is –sec is –csc is +cot is –cos is +sin is +tan is +sec is +csc is +cot is +xQuadrant IIIQuadrant IVcos is –sin is –tan is +sec is –csc is –cot is +cos is +sin is –tan is –sec is +csc is –cot is –For any given angle, a trig function and itsreciprocal have values with the same sign.
4Reciprocals – Graph of Cosecant reciprocal of 0- undefinedthereforethese are the only points of equalityf(x) = csc x
5Reciprocals – Graph of Secant reciprocal of 0undefinedthereforethese are the only points of equalityf(x) = sec x
6Reciprocals – Graph of Cotangent the only points of equalityf(x) = cot x-
7Model ProblemsWhich expression represents the exact value of csc 60o?Which expression gives the correct values of csc 60o?Which is NOT an element of the domain of y = cot x?
8Model ProblemsA handler of a parade balloon holds a line of length y. The length is modeled by the function y = d sec , where d is the distance from the handler of the balloon to the point on the ground just below the balloon, and is the angle formed by the line and the ground. Graph the function with d = 6 and find the length of the line needed to form an angle of 60o.
9Model ProblemGraph the function|a| = amplitude (vertical stretch or shrink)h = phase shift, or horizontal shiftk = vertical shift|b| = frequencydilationfrequencyphase shiftvertical shifta = 2b = 3k = -2