Section 7-5 The Other Trigonometric Functions

Objective: To find the values of: the tangent, cotangent, secant, and

cosecant functions and to sketch the functions’

graphs.

FILL IN THE TABLE BELOWQuadrant

I

II

III

IV

Topics to know for today’s lesson

State the reciprocal of each:

Divide each. Leave answers in exact form.

We can define other trig functions in terms of (x,y).

name Abbreviation definition

tangent of tan

cotangent of

cot

secant of sec

cosecant of csc

tan y

x

sec r

x

cot x

y

y

rcsc

Reciprocals

cotcos

sin

tan

sin

cos

cos

1sec

cscsin

1

cottan

1

Fill in the table below with appropriate signsQ1 Q2 Q3 Q4

tan

cot

sec

csc

Fill in the table below with appropriate signsQ1 Q2 Q3 Q4

tan + - + -

cot + - + -

sec + - - +

csc + + - -

Positive Negative

Find the value of each; round to the nearest

hunderdths

1. )

HINT: Make sure to use the proper mode.

RestrictionsFunction Definition restriction

Why do the restrictions matter

The value of the function on the calculator

The graph of the function.

Find the value of each expression to four significant digits.

A.) tan 203°

B.) cot 165°

C.) csc (-1)

D.) sec 11

Hint:

Express each in terms of reference angle:

1) csc 285°2) sec 749°3) csc -245°4) sec 5) csc

Sec 7.5 day 2Express each of the

following in terms of a reference angle.

Tangent and secant functions on unit circle.

BD represents themeasure of sec

DC represents themeasure of tan

D

EB C

A

Cotangent and cosecant on the unit circle

BF is the csc GF is cot

FG

EB C

A

Graph

-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π

-9-8-7-6-5-4-3-2-1

123456789

x

ytan θ

θin radians

What you should know about

1) Domain2) Range3) Period4) Asymptotes5) The connection between the

asymptotes and the definition of the .6) The connection between the

asymptotes and the values on the UC

Graph fundamental period

-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π

-9-8-7-6-5-4-3-2-1

123456789

x

ytan θ

θin radians

Graph

-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π

-9-8-7-6-5-4-3-2-1

123456789

x

y

θ radians

Sec θ why can’t be between -1 and 1?

What you should know about

1) Domain2) Range3) Period4) Asymptotes5) The connection between the

asymptotes and the definition of the .6) The connection between the

asymptotes and the values on the UC

Graph for one period

-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π

-9-8-7-6-5-4-3-2-1

123456789

x

y

If q was in degrees:

How would each graph be different?

How would each graph be the same?

What would the period and amplitude be?

Given θ is a second-quadrant angle If , find the values of the other five

trigonometric functions.

Homeworkwritten exercise sec 7.5

DAY 1: # 1-9 allDAY 2: #10-19 all and 23-27 odds

Optional:Check out: Graphing program online: DesmosOrhttp://www.padowan.dk/