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

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# Aim: How can we graph the reciprocal trig functions using the three basic trig ones? - PowerPoint PPT Presentation

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?

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

function

reciprocal

reciprocal

function

Trig Values in Coordinate Plane

y

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

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

reciprocal of 0

- undefined

therefore

these are the only points of equality

f(x) = csc x

Reciprocals – Graph of Secant

reciprocal of 0

undefined

therefore

these are the only points of equality

f(x) = sec x

Reciprocals – Graph of Cotangent

the only points of equality

f(x) = cot x

-

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 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.

|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 Problem

Graph the function

a = 2

b = 3

k = -2