34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2)...
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Transcript of 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2)...
![Page 1: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/1.jpg)
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
![Page 2: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/2.jpg)
Section 13.8
Reciprocal Trigonometric Functions
![Page 3: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/3.jpg)
PART 1
Evaluating Reciprocal Trigonometric Functions
![Page 4: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/4.jpg)
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
![Page 5: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/5.jpg)
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
![Page 6: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/6.jpg)
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
![Page 7: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/7.jpg)
Please complete exercises 1 – 27 odd starting on page 752
Homework (part 1)
![Page 8: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/8.jpg)
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
![Page 9: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/9.jpg)
PART 2
Graphing Reciprocal Trigonometric Functions
![Page 10: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/10.jpg)
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
![Page 11: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/11.jpg)
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
![Page 12: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/12.jpg)
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
![Page 13: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/13.jpg)
Please complete exercises 29– 40 starting on page 752
Homework (part 2)
![Page 14: 34) y = cos (x – 1.5)35) y = cos (x + 3/(2π)) 36) y = sin x –3π37) 38) y = sin (x – 2) –439) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.541) y = 2 cos.](https://reader036.fdocuments.us/reader036/viewer/2022082323/56649ee65503460f94bf7226/html5/thumbnails/14.jpg)
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