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**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 = 6 and mJMT = 90. What is the value of cot J? J M T

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**Reciprocal Identities**

Co- Co- Co-

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**Trig Values in Coordinate Plane**

y Quadrant II Quadrant I function reciprocal function reciprocal cos is – sin is + tan is – sec is – csc is + cot is – cos is + sin is + tan is + sec is + csc is + cot is + x Quadrant III Quadrant IV cos 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 its reciprocal have values with the same sign.

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**Reciprocals – Graph of Cosecant**

reciprocal of 0 - undefined therefore these are the only points of equality f(x) = csc x

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**Reciprocals – Graph of Secant**

reciprocal of 0 undefined therefore these are the only points of equality f(x) = sec x

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**Reciprocals – Graph of Cotangent**

the only points of equality f(x) = cot x -

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Model Problems Which 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?

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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 60o.

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Model Problem Graph the function |a| = amplitude (vertical stretch or shrink) h = phase shift, or horizontal shift k = vertical shift |b| = frequency dilation frequency phase shift vertical shift a = 2 b = 3 k = -2

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Model Problem Graph the function dilation frequency phase shift vertical shift a = 2 b = 3 k = -2

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4.4 Day 1 Trigonometric Functions of Any Angle –Use the definitions of trigonometric functions of any angle –Use the signs of the trigonometric functions.

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