34) y = cos (x – 1.5) 35) y = cos (x + 3/(2π))

36) y = sin x –3π 37)

38) y = sin (x – 2) –4 39) y = cos (x +3) + π

40) y = sin (x – π/2) + 3.5 41) y = 2 cos (x – π/3) –1

y = 2 sin (x + π/6) –1

42) y = 10 cos π/10(x – 10) 43) sin x = cos (x – π/2)

y = 10 sin π/10(x – 5) cos x = sin (x + π/2)

13.7 (part 2) answers

Section 13.8

Reciprocal Trigonometric Functions

PART 1

Evaluating Reciprocal Trigonometric Functions

We have studied sine, cosine, and tangent These functions are ratios (fractions) and have

reciprocals These reciprocals are cosecant (csc), secant

(sec), and cotangent (cot)

Reciprocals

Use the definitions of cosecant, secant and cotangent to find their values

They are the inverses of the sine, cosine and tangent values we already have

Evaluate each expression:

1. csc (80°)1.015

2. sec (200°)–1.064

3. If sin θ = 13/18, what is csc θ?

18/13

Calculating Values

Find the exact values of the following:

1) csc 60˚= 1/sin 60˚ = 2√(3)/3

2) sec 60˚= 1/cos 60˚ = 2

3) sec 210˚= 1/cos 210˚ = –2√(3)/3

If sin θ = 5/13, find the other 5 trig ratios of θ.

cos θ = 12/13 sec θ = 13/12

csc θ = 13/5

tan θ = 5/12 cot θ = 12/5

More Practice

θ

513

12

Please complete exercises 1 – 27 odd starting on page 752

Homework (part 1)

1) csc (100°) = 1.02 3) cot (–55°) = –0.70

5) cot θ = 15/20 7) sec θ = –35/21

9) sec (45°) = √2 11) cot (90°) = 0

13) csc (0°) = undefined 15) cot (0°) = undefined

17) sec (90°) = undefined 19) sec (60°) = 2

21) cot (3) = –7.02 23) csc (π/2) = 1

25) sec (2.5) = –1.25 27) cot (π/6) = 1.73

Homework (part 1) answers

PART 2

Graphing Reciprocal Trigonometric Functions

1) Begin with the normal function

2) Find the reciprocal of each output value

3) Plot the points of the reciprocal function

csc (x)

Undef

2

1

2

Undef

-2

-1

-2

Undef

Building a Table

x

0

π/6

π/2

5π/6

π

7π/6

3π/2

11π/6

2π

sin (x)

0

0.5

1

0.5

0

-0.5

-1

-0.5

0

Plotting the Graph of y = csc (x)

csc (x)

Undef

2

1

2

Undef

-2

-1

-2

Undef

x

0

π/6

π/2

5π/6

π

7π/6

3π/2

11π/6

2π

π

1

We can use the calculator to find approximate values from graphs

We can do it using the <TRACE> or the <TABLE> feature

Begin by entering the function into Y1

Use the <TRACE> feature to find the following. Round your answer to the 4th decimal place.

1) sec (50°)1.5557

2) sec (105°)-3.8637

3) csc (82°)1.0098

4) cot (20°)2.7475

Using the Calculator

Please complete exercises 29– 40 starting on page 752

Homework (part 2)

29) 30)

31) 32)

33) 1.1547 34) 5.7588 35) -2.9238 36) 2

37) 1.0642 38) 1.3054 39) 1.7321 40) 0.5774

Homework (part 2) answers