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Mathematics

Formulas

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Closure Property of Addition Sum (or difference) of 2 real numbers equals a real number Additive Identity a + 0 = a Additive Inverse a + (-a) = 0 Associative of Addition (a + b) + c = a + (b + c) Commutative of Addition a + b = b + a Definition of Subtraction a - b = a + (-b) Closure Property of Multiplication Product (or quotient if denominator 0) of 2 reals equals a real number Multiplicative Identity a * 1 = a Multiplicative Inverse a * (1/a) = 1 ? ? (a 0) (Multiplication times 0) a * 0 = 0 Associative of Multiplication (a * b) * c = a * (b * c) Commutative of Multiplication a * b = b * a Distributive Law a(b + c) = ab + ac Definition of Division a / b = a(1/b)

Trigonometry Reference Chart

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The unit circle is a commonly used tool in trigonometry because it helps the user to remember the special angles and their trigonometric functions. The unit circle is a circle drawn with its center at the origin of a graph(0,0), and with a radius of 1. All angles are measured starting from the x-axis in quadrant one and may go around the unit circle any number of degrees. Points on the outside of the circle that are in line with the terminal (ending) sides of the angles are very useful to know, as they give the trigonometric function of the angle through their coordinants. The format is (cos, sin). Note that in trigonometry, an angle can be of any size, positive or negative. An angle larger than 360º means that you have gone round the circle more than once.

Algebra Formulas

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Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn a0 = 1 (am)/(an) = am-n a-m= 1/(am) Quadratic Formula In an equation like ax2 + bx + c = 0 You can solve for x using the Quadratic Formula: Binomial Theorem (a + b)1 = a + b (a + b)2 = a2 + 2ab + b2 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 ...and so on... Difference of Squares a2 - b2 = (a - b)(a + b) Rules of Zero 0/x = 0 where x is not equal to 0. a0 = 1 0a = 0 a*0 = 0 a/0 is undefined (you can't do it)

Exponents

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Since an exponent on a number indicates multiplication by that same number, an exponent on a negative number is simply the negative number multiplied by itself a certain number of times: (- 4)3 = - 4× -4× - 4 = - 64 (- 4)3 = - 64 is negative because there are 3 negative signs--see Multiplying Negatives. (- 5)2 = - 5× - 5 = 25 (- 5)2 = 25 is positive because there are 2 negative signs.

Inverses of Trigonometric Ratios

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Inverses of Trigonometric Ratios You've learned how to use trig ratios to solve right triangles, finding the lengths of the sides of triangles. But what if you have the sides, and need to find the angles? You know that you can take side lengths and find trig ratios, and you know you can find trig ratios (in your calculator) for angles. What is missing is a way to go from the ratios back to the original angles. And that is what "inverse trig" values are all about. If you look at your calculator, you should see, right above the "SIN", "COS", "TAN" buttons, notations along the lines of "SIN–1", "COS–1", and "TAN–1", or possibly "ASIN", "ACOS", and "ATAN". These are what you'll use to find angles from ratios.

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