feb 24 25 trigonometry 1
TRANSCRIPT
Trigonometry!
hypotenuseop
posi
te
adjacent
sin = o/hcos = a/htan = o/a
Coordinate Geometry!
O(0,0)
O = originA(3,2)
B(-3,-2)
Trigonometry + Coordinate Geometry!!
A(5,4)
What angle does a line drawn from the origin to point A(5,4) make with the x axis?
terminal arm
5
4
52 + 42 = h2
25+16 = h2
√61 = h
tan = 4/5
= 38.66
draw a terminal arm to Z(6,7)
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
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
draw the terminal arm at 120
related angle ( ) is measured to the x axis in the same quadrant.
θr is always measured from the x axis
P(-5,4)
Q(-4,-6)
A(2,3)
B(8,-9)
If sin = 1/2, find all possible values of
1221θ1 = 30˚
θ2 = 150˚
θr = 30°
Related angle = θr
θr is always measured from the closest x axis
θrθr
θrθr
θ= 260°
θr
θr = 260° - 180° = 80°
Exercise 81-6 new stuff11 and 13 = good review for test
Exercise 91, 10, 11, 12 new stuff4, 9 = good review for the test
cosθ= -12
θr
θr-1
2
θr-1
2
θ1 = 120°
θ2 = 240°
θr= 60°
sinθ= - 23
θr2
3
θr2
3
θ1= 221.81
θ2= 318.2
θr2
3
θr = 41.81
tanθ= - 12
θ1 = 153.44
θ2= 333.441
2
θr= 26.56
III
III IV
Find all possible values of θ, such that sin θ = 1/2, for the interval {0° ≤θ ≤ 360°}
1 2