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Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Do Now: Aim: How can we graph the reciprocal trig functions using the three basic trig ones?

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Presentation on theme: "Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Do Now: Aim: How can we graph the reciprocal trig functions using the three basic trig ones?"— Presentation transcript:

1 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Do Now: Aim: How can we graph the reciprocal trig functions using the three basic trig ones? In the diagram below of right triangle JMT, JT = 12, JM = 6 and m JMT = 90. What is the value of cot J? J M T

2 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Reciprocal Identities Co-

3 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Trig Values in Coordinate Plane y Quadrant IQuadrant II function reciprocal x sec is + csc is + cot is + sec is + csc is – cot is – cos is + sin is + tan is + cos is + sin is – tan is – Quadrant IVQuadrant III cos is – sin is + tan is – cos is – sin is – tan is + For any given angle, a trig function and its reciprocal have values with the same sign. sec is – csc is – cot is + sec is – csc is + cot is –

4 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Reciprocals – Graph of Cosecant reciprocal of 0- undefined therefore these are the only points of equality f(x) = csc x

5 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Reciprocals – Graph of Secant reciprocal of 0undefined therefore these are the only points of equality f(x) = sec x

6 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Reciprocals – Graph of Cotangent the only points of equality f(x) = cot x -

7 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Model Problems Which expression represents the exact value of csc 60 o ? Which expression gives the correct values of csc 60 o ? Which is NOT an element of the domain of y = cot x?

8 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Model Problems A 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 60 o.

9 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Model Problem Graph the function |a| = amplitude (vertical stretch or shrink) h = phase shift, or horizontal shift k = vertical shift |b| = frequency dilationfrequencyphase shiftvertical shift a = 2b = 3 k = -2

10 Aim: Graphs of Reciprocal Functions Course: Alg. 2 & Trig. Model Problem Graph the function dilationfrequencyphase shiftvertical shift a = 2b = 3 k = -2


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