ccny pre calc exam 4

9.1-11.5

tan

sin/cos

cot

cos/sin

sin²+cos²

1

tan²+1

sec²

cot²+1

csc²

cos(a+b)

cosacosb-sinasinb

cos(a-b)

cosacosb+sinasinb

sin(a+b)

sinacosb+cosasinb

sin(a-b)

sinacosb-cosasinb

sin(2θ)

2sinθcosθ

cos(2θ) (1)

cos²θ-sin²θ

cos(2θ)

1-2sin²θ

cos(2θ)

2cos²θ-1

sin (θ/2)

±√(1-cosθ)/2

cos(θ/2)

±√(1+cosθ)/2

pi/3

pi/3, 2pi/3, 4pi/3, 5pi/3

pi/4

pi/4, 3pi/4, 5pi/4, 7pi/4

pi/6

pi/6, 5pi/6, 7pi/6, 11pi/6

0

0, pi/2, pi, 3pi/2

Distance formula

√ (x2-x1)²+(y2-y1)²

Midpoint formula

((x1+x2)/2, (y1+y2)/2)

Equation of a circle

(x-h)²+(y-k)²=r²

Standard form equation of an ellipse with center (0,0)

x²/a²+y²/b²=1

Standard form equation of an ellipse with center (h,k)

(x-h)²/a²+(y-k)²/b²=1