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Aim: How can we graph the reciprocal trig functions using the three basic trig ones?

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 m JMT = 90. What is the value of cot J?. J. M. T. Reciprocal Identities. Co-. Co-. Co-. function. reciprocal. reciprocal.

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Aim: How can we graph the reciprocal trig functions using the three basic trig ones?

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  1. 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 mJMT = 90. What is the value of cot J? J M T

  2. Reciprocal Identities Co- Co- Co-

  3. function reciprocal reciprocal function Trig Values in Coordinate Plane y Quadrant II Quadrant I 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.

  4. Reciprocals – Graph of Cosecant reciprocal of 0 - undefined therefore these are the only points of equality f(x) = csc x

  5. Reciprocals – Graph of Secant reciprocal of 0 undefined therefore these are the only points of equality f(x) = sec x

  6. Reciprocals – Graph of Cotangent the only points of equality f(x) = cot x -

  7. 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?

  8. 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.

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

  10. Model Problem Graph the function a = 2 b = 3 k = -2

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