Math Concepts Flashcards
degree to radian conversion
radians = degree (π/180º)
π in this calculation is 3.14
or π radians = 180º
radian to degree conversion
degree = radian (180º/π)
π in this calculation is 3.14
or π radians = 180º
what is π in degrees? 2π?
π = 180º, 2π = 360º
10^-x = ?
1/10^x
exponent law: b^-p = ?
b^-p = 1/10^p
ex: 10^-7 = 1/10^7
log(2)y=-3 -> y = 2^-3, y = 1/8
square root law
x√a^y = a^(y/x)
simple way to add/subtract fractions
a/b + c/d = ad - bc/bd
a/b - c/d = ad - bc/bd
rule for solving for > and < signs
flip sign when rearranging equation (multiplying, don;t have to when just adding)
quadrants in a graph
upper right is Q1, then go counterclockwise
3 special triangles
1,1,√2 (45º, 45º, 90º)
1,2,√3 (30º, 90º, 60º)
3,4,5 (37º, 53º, 90º)
what is sin60º and cos30º
√3/2
what is inverse (sin/cos/tan)
for example: sin-1 (1/2) = 30º
what is tanθ?
tanθ = sinθ/cosθ
what must a graph of direct proportion look like?
It must go through the origin and be a linear increase.
rearrange b^a=c in log form
log(b)c = a
rearrange log(b)c=a
b^a = c
what is log 1?
0
what is a natural log (ln)?
lny = log(e)y = log(2.7)y
2.7^x=y
how to deal with log exponents (logY^z)
logY^z = zlogY
with bases the same
how to deal with multiplication/division of logs
log(yz) = log(y) + log(z)
log(y/z) = log(y) - log(z)
with bases the same
what is y = x^1/2
x^1/2 = √x 16^1/2 = 4
what are the acid/base log rules?
1-3 x 10^-5 = pH btw 4 and 5 (closer to 5)
3 x 10^-5 = pH at 4.5
3-9 x 10^-5 = pH btw 4 and 5 (closer to 4)
