Download Section 13.8 - MitchellAlg3H

13.7 (part 2) answers
34) y = cos (x – 1.5)
36) y = sin x –3π
35) y = cos (x + 3/(2π))
37)
38) y = sin (x – 2) –4
40) y = sin (x – π/2) + 3.5
39) y = cos (x +3) + π
41) y = 2 cos (x – π/3) –1
y = 2 sin (x + π/6) –1
43) sin x = cos (x – π/2)
cos x = sin (x + π/2)
42) y = 10 cos π/10(x – 10)
y = 10 sin π/10(x – 5)
Section 13.8
Reciprocal Trigonometric Functions
Evaluating Reciprocal Trigonometric Functions
PART 1
Reciprocals
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)

Calculating Values


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
More Practice
Find the exact values of the
following:
1)
csc 60˚
If sin θ = 5/13, find the other
5 trig ratios of θ.
= 1/sin 60˚ = 2√(3)/3
13
2)
sec 60˚
θ
12
= 1/cos 60˚ = 2
cos θ = 12/13
3)
sec 210˚
= 1/cos 210˚ = –2√(3)/3
5
tan θ = 5/12
sec θ = 13/12
csc θ = 13/5
cot θ = 12/5
Homework (part 1)
Please complete exercises 1 – 27 odd starting on
page 752
Homework (part 1) answers
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
Graphing Reciprocal Trigonometric Functions
PART 2
Building a Table
1)
2)
3)
Begin with the normal
function
Find the reciprocal of
each output value
Plot the points of the
reciprocal function
x
sin (x)
csc (x)
0
0
Undef
π/6
0.5
2
π/2
1
1
5π/6
0.5
2
π
0
Undef
7π/6
-0.5
-2
3π/2
-1
-1
11π/6
-0.5
-2
2π
0
Undef
Plotting the Graph of y = csc (x)
x
csc (x)
0
Undef
π/6
2
π/2
1
5π/6
2
π
Undef
7π/6
-2
3π/2
-1
11π/6
-2
2π
Undef
1
π
Using the Calculator



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
Homework (part 2)
Please complete exercises 29– 40 starting on
page 752
Homework (part 2) answers
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