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Math Definitions
Pre Calc Moynihan
| Term | Definition |
|---|---|
| A Solution to a System of Equations | a marganized pair that satisfies every pair in a system |
| Plugging in the Derivative gives us | The Slope of a line tangent to a curve The instantaneous rate of change of a function |
| A Limit | the y-value that the function approaches as x gets infinitely closer to a given point |
| A Logarithm | the exponent to which the base is raised to get the number |
| Function | a rule of correspondence between 2 sets, the domain and the range, such that for every element of the domain there is exactly one element of the range |
| a²-b² | (a-b)(a+b) |
| a³+b³ | (a+b)(a²-ab+b²) |
| a³-b³ | (a-b)(a²+ab+b²) |
| Slope Formula | (y2-y1)/(x2-x1) |
| log(MN) | logM+logN |
| log(M/N) | logM-logN |
| log(M^k) | klogM |
| Trig Pythagorean Identities | sin²x+cos²x=1 1+tan²x=sec²x 1+cot²x=csc²x |
| Trig Tangent Identities | tan=sin/cos cot=cos/sin |
| Trig Sum and Differance Identities | sin(A±B)=sinAcosB±cosAsinB cos(A±B)=cosAcosB■sinAsinB |
| Trig Double Angel Identities | sin2x=2sinxcosx cos2x=cos²x-sin²x=2cos²x-1=1-2sin²x |
| The Arc of an angle | The angle whose ______ is _______ |
| Formula for Trig Graphs | y = c + a (sin/cos) k(x-s) c= center line k = period a = amplitude s = left/right shirt |
| Derivative of e^x | e^x |
| Derivative of ln x | 1/x |
| Derivative of Sin x | cos x |
| Derivative of Cos x | -sin x |
| Derivative of f(x) = g(x)h(x) Product Rule | f^1(x) = g(x)h^1(x) + h(x)g^1(x) *REMEMBER TO TREAT THESE AS SUCH: XSINX* |
| Derivative of f(x) = g(x)/h(x) Quotient Rule | low d high - high d low over the square of whats below |
| general Form | ax +by =c |
| point slope form | y - ysub1 = m(x - xsub1) |
| parallel lines | m1 =m2 |
| perpendicular lines | m1 = -1/m2 |
| Origin Symmetry | all exponents are odd |
| Y axis Symmetry | all exponents are even |
| Horizontal line test | Sees if a function is 1 to1 |
| Vertical line test | Sees if a function |
| Trig Cofunction Identitys | sin(90°-x) =cos x cos(90°-x) = sin x tan(90°-x) = cot x cot(90°-x) = tan x sec(90°- x) = csc x csc(90°- x) = sec x |