1. 13.7 (part 2) answers
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) ) 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)

2. Reciprocal Trigonometric Functions
Section 13.8
Reciprocal Trigonometric Functions

3. Evaluating Reciprocal Trigonometric Functions
Part 1

4. 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)

5. 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:
csc (80°)
1.015
sec (200°)
–1.064
If sin θ = 13/18, what is csc θ?
18/13

6. More Practice csc 60˚ sec 60˚ sec 210˚
Find the exact values of the following:
csc 60˚
= 1/sin 60˚ = 2√(3)/3
sec 60˚
= 1/cos 60˚ = 2
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 13 5 θ 12

7. Please complete exercises 1 – 27 odd starting on page 752
Homework (part 1)
Please complete exercises 1 – 27 odd starting on page 752

8. Homework (part 1) answers
1) csc (100°) = ) 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) = – ) csc (π/2) = 1 25) sec (2.5) = – ) cot (π/6) = 1.73

9. Graphing Reciprocal Trigonometric Functions
Part 2

10. Building a Table Begin with the normal function
Find the reciprocal of each output value
Plot the points of the reciprocal function x
π/6
π/2
5π/6 π
7π/6
3π/2
11π/6 2π
sin (x)
0.5 1
-0.5 -1
csc (x)
Undef 2 1 -2 -1

11. Plotting the Graph of y = csc (x)π x
π/6
π/2
5π/6 π
7π/6
3π/2
11π/6 2π
csc (x)
Undef 2 1 -2 -1 1

12. 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.
sec (50°)
1.5557
sec (105°)
csc (82°)
1.0098
cot (20°)
2.7475

13. Please complete exercises 29– 40 starting on page 752
Homework (part 2)
Please complete exercises 29– 40 starting on page 752

14. Homework (part 2) answers
29) 30) 31) 32) 33) ) ) ) 2 37) ) ) )