Conics
What is the equation of a circle?
(x - h)² + (y - k)² = r²
What is another way you can write log216=4
24=16
sin-1(1)
π/2
f(b)-f(a)/b-a
How do you find the period of a sine function?
Period=2π /b
Identify the conic section and the center:
(x-8)2/49+(y-2)2/9=1
An ellipse with a center of (8,2).
Solve:
4+log4x=8
x=256
cos-1(tan(3π/4))
π
What is happening to the ROC if a function is concave down? Concave up?
If the function is concave down, the ROC is decreasing, and if it is concave up, the ROC is increasing.
tan (7π)
0
What is the specific type of parabola, given the equation:
y+3=1/7(x-4)2
Vertical parabola, because the (x-4) is being squared.
Solve:
log3(8x+9)=4
x=9
cos-1(0)
π/2
3π/2 on the unit circle is equivalent to how many degrees?
270 degrees
What quadrant can each inverse trig function come from?
sin-1x
cos-1x
tan-1x
sin-1x: 1 and 4
cos-1x: 1 and 2
tan-1x: 1 and 4
How do you find the p value of a parabola?
1/4p=a
Solve:
log5(4x+12)=log5(x+7)
x=-5/3
arcsin(square root of 2/2)
π/4
What is this equation used for?
A(t)=aert
Continuous growth and decay
cot (5π/3)
Square root of -3/3
Complete the square in order to then determine the conic section:
x2+6x+8y+1=0
(x+3)2=-8(y-1)
Parabola
Solve:
log6(3x+14)-log65=log62x
Hint: This uses one of the condensing rules.
x=2
cos(sin-1(1/2))
Square root of 3/2
What is the domain and range of a logarithmic function?
D: (0,∞)
R: (-∞, ∞)
What are the three Pythagorean Identities?
sin²(θ) + cos²(θ) = 1
1+cot2x=csc2x
1+tan2x=sec2x