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Trig 2640
special angles and trig equations and identities
| Question | Answer |
|---|---|
| Sin 0 | 0 |
| Cos 0 | 1 |
| Tan 0 | 0 |
| Sin pi/6 | 1/2 |
| Cos pi/4 | Square root of 2/2 |
| Tan pi/6 | Square root of 3/3 |
| Cos pi/6 | Square root of 3/2 |
| Sin pi/4 | Square root of 2/2 |
| Tan pi/4 | 1 |
| Sin pi/3 | Square root of 3/2 |
| Cos pi/3 | 1/2 |
| Tan pi/3 | Square root 3 |
| Sin pi/2 | 1 |
| Cos pi/2 | 0 |
| Tan pi/2 | Undefined |
| Sum formula for Sin | SinACosB+CosASinB |
| Sum formula for Cos | CosACosB-sinAsinB |
| Sum formula for Tan | tanA+tanB/1-tanAtanB |
| Difference Formula for sin | sin(A-B)= sinAcosB-cosAsinB |
| Double angle formula for sin | sin(2A)= 2sinAcosA |
| half-angle formula for sin | sin(A/2)= (+-)Square root of (1-cosA/2) |
| tanA | sinA/cosA |
| cotA | cosA/sinA |
| Pythagorean identity 1 | sin^2(A) + cos^2(A) = 1 |
| Law of sines | a/sinA = b/sinB = c/sinC |
| Law of cosine | a^2 = b^2 + c^2 - 2bc cosA |
| Parabola: formulas | Formulas: y^2 = 4px when parabola on x-axis x^2 = 4py when parabola on y-axis |
| Ellipse: formula | formula: (x^2/a^2) + (y^2/b^2) = 1 |
| Hyperbola: formulas | Formulas: (x^2/a^2) - (y^2/b^2) = 1 |
| double angle formula for cos | cos(2A)= cos^2(A)-sin^2(A) |
| double angle formula for tan | tan(2A)= 2tanA/1-tanA |
| Difference Formulas for cos | cos(A-B)= cosAcosB+sinAsinB |
| Difference Formulas for tan | tan(A-B)= tanA-tanB/1+tanAtanB |
| half-angle formula for cos | cos(A/2)= square root of (1+cosA/2) |
| half-angle formula for tan | tan(A/2)= square root of (1-cosA/1+cosA) |
| Pythagorean identity 2 | tan^2(A) + 1 = sec^2(A) |
| Pythagorean identity 3 | 1 + cot^2(A)= csc^2(A) |
| Parabola: Foci | for when on x-axis (p,0) for when on y-axis (0,p) |
| Ellipse: Foci | when a is bigger ((+-) square root of (a^2 - b^2), 0) when b is bigger (0, (+-) square root of (b^2 - a^2)) |
| Hyperbola: Foci | When on x-axis, ((+-) square root of (a^2 + b^2), 0) When on y-axis, (0, (+-)square root of (b^2+a^2)) |
| y = f(x) + c | Vertical shift c units up |
| y = f(x) - c | Vertical shift c units down |
| y = f(x + c) | Horizontal shift c units to the left |
| y = f(x - c) | Horizontal shift c units to the right |
| y = -f(x) | Reflection over x-axis |
| y = f(-x) | Reflection over y-axis |
| y = cf(x) | vertical stretch/shrink, when c > 1 it's stretch, (x,y)--> (x,y*c) |
| y = f(cx) | horizontal stretch/shrink, c < 1 it's shrink, (x,y)--> (x*(1/c),y) |
| a^0 = | 1 |
| a^-n = | 1/a^n |
| a^m(a^n) = | a^(m+n) |
| a^m/a^n = | a^(m-n) |
| (a^m)^n = | a^m*n |
| (ab)^n = | (a^n)b^n |
| log base a of 1 = | 0 |
| log base a of a = | 1 |
| log base a of a^n = | n |
| a^log base a of x = | x |
| log base a of (UV) = | log base a of U + log base a of V |
| log base a of (u/v) = | log base a of u - log base a of v |
| log base a of u^n = | n*log base a of U |
| log base a of U = | log base b of U/ log base b of a |
Created by:
burtond
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