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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 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
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

trig values in coordinate plane

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.

reciprocals graph of cosecant
Reciprocals – Graph of Cosecant

reciprocal of 0

- undefined

therefore

these are the only points of equality

f(x) = csc x

reciprocals graph of secant
Reciprocals – Graph of Secant

reciprocal of 0

undefined

therefore

these are the only points of equality

f(x) = sec x

reciprocals graph of cotangent
Reciprocals – Graph of Cotangent

the only points of equality

f(x) = cot x

-

model problems
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?

model problems1
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.

model problem

|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

model problem1
Model Problem

Graph the function

a = 2

b = 3

k = -2