Math Flashcards
Trigonometric ratio mnemonic from a known angle
soh cah toa
sine = opposite/hypotenuse cosine = adjacent/hypotenuse tangent = opposite/adjacent
Factoring a sum of cubes
a3 + b3
x3+ 1
Formula: (a+b)(a2-ab+b2)
a3 + b3 = (a+b)(a2-ab+b2)
x3 + 1 = (x + 1)(x2-1x+12)
Cosecant
csc(x) =
Reciprocal of sine
csc(x) = 1/sin(x)
csc = hypotenuse/opposite side
Secant
sec(x) =
Receiprocal of cosine
sec(x) = 1/cos(x)
sec = hypotenuse/adjacent side
Cotangent
cot(x) =
The reciprocal of tangent
cot(x) = cos(x)/sin(x)
cot = adjacent/opposite side
sec(0) =
1
What is a natural log?
ln
The natural logarithm of a number is its logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828.
What is relationship of tangent with cosine, and sine?
tan = sin/cos
1/(2/5) =
5/2
What is a similar triangle?
Corresponding angles are congruent (equal). One triangle is simply a scaled (up/down) version of the other. All sides are scaled by the same factor.
(Denoted: Triangle ABC ~ Triangle DEF)
Negative exponents
4-3 = ?
1/43 = 1/64
You take the reciprocal of the coefficient to the positive exponent. [e.g. (3/2)-2 = (2/3)2]
Fractional Exponents
41/2 = ?
sqrt(4) = 41/2
(or cube root of 8 = 81/3)
Multiplying values with exponents.
x5* x3 = ?
Add the exponents
x5+3 = x8
Raising an exponent
(3a)5 = ?
Multiply the exponents
(3a)5 = 35a
Fractions raised to a power:
(3/2)3 = ?
(3/2)3 = 33/23
Simplify
(5d)1/2= ?
(5d)1/2 = 51/2 * d1/2
It is equivalent to taking each term to that exponent. Same with division.
What is the relationship between sine and cosine?
sin x = cos (90-x)
Sine of an angle is equal to cosine of its complementary angle in the right triangle. (sin 32° = cos 58°)
Simplify
x-2/3
x-2/3 = 1/x2/3
x2/3 = (x2*1/3) = (x2)1/3
= cubrt(x2)
In other words: denominator root of x to the power of the numerator.
