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