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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.

Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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Page 1: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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.

Page 2: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

FILL IN THE TABLE BELOWQuadrant

I

II

III

IV

Page 3: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Topics to know for today’s lesson

State the reciprocal of each:

Divide each. Leave answers in exact form.

Page 4: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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

Page 5: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Reciprocals

cotcos

sin

tan

sin

cos

cos

1sec

cscsin

1

cottan

1

Page 6: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Fill in the table below with appropriate signsQ1 Q2 Q3 Q4

tan

cot

sec

csc

Page 7: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Fill in the table below with appropriate signsQ1 Q2 Q3 Q4

tan + - + -

cot + - + -

sec + - - +

csc + + - -

Positive Negative

Page 8: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the
Page 9: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Find the value of each; round to the nearest

hunderdths

1. )

HINT: Make sure to use the proper mode.

Page 10: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

RestrictionsFunction Definition restriction

Page 11: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Why do the restrictions matter

The value of the function on the calculator

The graph of the function.

Page 12: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Find the value of each expression to four significant digits.

A.) tan 203°

B.) cot 165°

C.) csc (-1)

D.) sec 11

Hint:

Page 13: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the
Page 14: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Express each in terms of reference angle:

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

Page 15: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Sec 7.5 day 2Express each of the

following in terms of a reference angle.

Page 16: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Tangent and secant functions on unit circle.

BD represents themeasure of sec

DC represents themeasure of tan

D

EB C

A

Page 17: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

Cotangent and cosecant on the unit circle

BF is the csc GF is cot

FG

EB C

A

Page 18: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the
Page 19: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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

Page 20: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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

Page 21: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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

Page 22: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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?

Page 23: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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

Page 24: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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

Page 25: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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?

Page 26: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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

trigonometric functions.

Page 27: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the

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/

Page 28: Section 7-5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the