feb 24 25 trigonometry 1
TRANSCRIPT
![Page 1: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/1.jpg)
Trigonometry!
![Page 2: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/2.jpg)
hypotenuseop
posi
te
adjacent
sin = o/hcos = a/htan = o/a
![Page 3: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/3.jpg)
Coordinate Geometry!
![Page 4: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/4.jpg)
O(0,0)
O = originA(3,2)
B(-3,-2)
![Page 5: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/5.jpg)
Trigonometry + Coordinate Geometry!!
![Page 6: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/6.jpg)
A(5,4)
What angle does a line drawn from the origin to point A(5,4) make with the x axis?
terminal arm
![Page 7: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/7.jpg)
5
4
52 + 42 = h2
25+16 = h2
√61 = h
tan = 4/5
= 38.66
![Page 8: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/8.jpg)
draw a terminal arm to Z(6,7)
![Page 9: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/9.jpg)
6
7
what are the exact values of sin , cos , tan
sin = 7/√85
cos = 6/√85
tan = 7/6
62 + 72 = h2
36+49 = h2h = √85
√85
![Page 10: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/10.jpg)
If you are given an angle with no other information you can draw a terminal arm. Starting from the +ve x axis rotate the given degrees
![Page 11: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/11.jpg)
draw the terminal arm at 120
related angle ( ) is measured to the x axis in the same quadrant.
![Page 12: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/12.jpg)
θr is always measured from the x axis
P(-5,4)
Q(-4,-6)
A(2,3)
B(8,-9)
![Page 13: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/13.jpg)
If sin = 1/2, find all possible values of
1221θ1 = 30˚
θ2 = 150˚
θr = 30°
![Page 14: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/14.jpg)
Related angle = θr
θr is always measured from the closest x axis
θrθr
θrθr
![Page 15: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/15.jpg)
θ= 260°
θr
θr = 260° - 180° = 80°
![Page 16: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/16.jpg)
Exercise 81-6 new stuff11 and 13 = good review for test
Exercise 91, 10, 11, 12 new stuff4, 9 = good review for the test
![Page 17: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/17.jpg)
cosθ= -12
θr
θr-1
2
θr-1
2
θ1 = 120°
θ2 = 240°
θr= 60°
![Page 18: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/18.jpg)
sinθ= - 23
θr2
3
θr2
3
θ1= 221.81
θ2= 318.2
θr2
3
θr = 41.81
![Page 19: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/19.jpg)
tanθ= - 12
θ1 = 153.44
θ2= 333.441
2
θr= 26.56
![Page 20: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/20.jpg)
III
III IV
![Page 21: Feb 24 25 Trigonometry 1](https://reader033.vdocuments.us/reader033/viewer/2022052621/558c1750d8b42add718b457d/html5/thumbnails/21.jpg)
Find all possible values of θ, such that sin θ = 1/2, for the interval {0° ≤θ ≤ 360°}
1 2