Study Flashcards
For an angle θ, pick point P=(x,y) on its terminal side. Then:
r= √x^2 + y^2
If P is a point on the circle x^2+y^2=1 (unit circle), then
sin θ=y and cos θ=x and
sin^2 θ + cos^2 θ = 1
For π/2 < θ < π
θ’ = π - θ
θ’ = π - θ
For π/2 < θ < π
For π < θ < 3π/2
θ’ = θ - π
θ’ = θ - π
For π < θ < 3π/2
For 3π/2 < θ < 2π
θ’ = 2π - θ
θ’ = 2π - θ
For 3π/2 < θ < 2π
Complementary angles add to
90 degrees
Add to 90 degrees
Complementary angles
Supplementary angles add to
180 degrees
Add to 180 degrees
Supplementary
For 30 60 90 triangles on unit circle
√3 is x, 1 is y, 2 is hypotenuse
√3 is x, 1 is y, 2 is hypotenuse
For 30 60 90 triangles on unit circle
For 45 45 90 triangles unit circle
1 as x, 1 as y, √2 as hypotenuse
1 as x, 1 as y, √2 as hypotenuse
For 45 45 90 triangles unit circle
Positive trigonometric functions 4 quadrants
ASTC
Ordered pairs
π/6 or 30: (√3/2, 1/2)
π/4 or 45: (√2/2, √2/2)
π/3 or 60: (1/2, √3/2)
π/6 or 30: (√3/2, 1/2)
π/4 or 45: (√2/2, √2/2)
π/3 or 60: (1/2, √3/2)
Ordered pairs
Order of transformations
V shift H shift R x R y V stretch H stretch
V shift H shift R x R y V stretch H stretch
Order of transformations
When ln or log equations = 0
Put both equations on one side
