Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
tan sin cos sec 1 cos csc 1 sin cot cos sin sin cos 2 2 sin 2 1 cos 2 cos 2 1 sin 2 1 tan 2 sec 2 1 cot 2 csc 2 sin 2 cos 2 tan 2 Use your FORMULA SHEET!!!!! We use law of cosines when we have ______s.a.s._________ or ______s.s.s.____________. r e g 2egCosR 2 2 2 Use law of sines when asked to find the number of triangles that can be constructed. j a sin J sin A Axis of symmetry equation: Turning point b x 2a Plug in to find y! Sum of the roots: b a Product of the roots: c a Quadratic formula: b b 4ac x 2a 2 Use this when asked for: a+bi, simplest radical form or to a decimal place. i i 1 i i i (Divide exp. By 4) 2 3 1 i 0 Completing the square: 1. Subtract/add over the constant. 2. Factor out the coefficient of the x^2 and x term, if there is one. 3. Take half of the coefficient of the x term and square it and add it to that side, and also add it to the other side. 4. Factor the trinomial you made. 5. Solve for y (or x), whichever they ask for. ex. y 3x 12x 7 2 Discriminant is used to determine the types of roots: Rational, irrational, equal or imaginary b 4ac 2 If: b2 4ac 0, roots are rational and equal b 4ac 0, imaginary roots. 2 b 2 4ac 0, roots are real, unequal and rational (if it's a perfect square) b 4ac 0, real, irrational, unequal (if it's not a perfect square) 2 Conic sections: 1. circle ax ay r 2 4. parabola 2 ax by c or xy k 2 y ax bx c 2 3. hyperbola 2 2 Distance Formula: d x1 x2 y1 y2 2 *used to find lengths of line segments* 2 Midpoint formula: x1 x2 y1 y2 , 2 2 *used to find the midpoint* y y 1 2 Slope: x1 x2 s r Theta must be in radians. Inequalities: # line, use test points. If <, then shade between endpoints. If >, then shade outside endpoints. To find the inverse of a Function: 1.Switch the x and y 2.Solve for y 3. If graphing, go to table and switch the x and y. Inverse variation: Multiply, do not set up a proportion! Products equal. xy=xy Direct variation: x x y y Exponential growth and decay. amount after time t=initial amount(1 rate) y ab Remember to change y a(1 r) or t time x percents by moving decimal to the left 2 places. Don’t forget to keep the “e”: y Pe rt This is used when there is Continuous growth. You can only solve exponential equations, log equations must be written Exponential form first! Find a common base or log Both sides to solve! log b x p b x p Log form to: exponent form log ab log a log b a log log a log b b log a n log a 1 log x log x 2 n Fractional exponents: 3 2 x x 3 Power over root!!! Bottom number in the notch! COfunctions: angles add up to 90. complementary sin 30 = cos 60 tan 14 = cot 76 sec 3 = csc 87 y asinb(x c) d d is the midline Vert.shift a is the amplitude b is the Number of curves from 0 to 2 c is the Phase shift 2 p b Period is the length of one curve. 1 arcsin x is the same as sin x We are looking for the angle!!, 2nd calc sin …..etc…. Remember when solving trig Equations, find all quadrants. Force problems – remember to find the top angle. And no, the resultant does not bisect the angle, only in a rhombus!! Area of a non-right triangle Formula sheet!!!!! 1 k ab sin c 2 Must have 2 sides and the Included angle! If you see any of these, use your FORMULA SHEET. Binomial expansion: st nCr(1 term) n r nd (2 term) r Plug in the numbers and add them all up! Statistics and the Bell Curve: Use your formula sheet! Mean, median, mode and standard deviation, use stats and 1-var stats in your calculator. X For populations Sx For samples If you are asked to find the normal approximation and not given the mean or s.d. use these formulas and your calculator: mean np and std.dev.= npq normalcdf (low #, upper #, mean, std .dev.) X X is the mean is the population standard deviation S x is the sample standard deviation All of these are found in 1 var-stat L1,L2 when asked to graph a complex number: a+bi, graph it as you would the point (a,b) and then draw an arrow from the origin to the point. Ex. Find the sum of 3+4i and -2+i, then graph the sum. If asked to find the length of a + bi: a b 2 2 Y=sin x Y=cos x You must know the domain and range for the inverse trig. functions: 1 y sin x, D : 1 x 1 R: 2 y 2 1 y cos x, D : 1 x 1 R: 0 y 1 y tan x, D : all reals R: 2 y 2 Laws of Exponents: x x x a b ab a x ab x b x a b ab (x ) x 1 a x a x Remember, anything raised to the zero power is one. Fractional Exponents: r b b p p r Fractional Equations: Find where denom. =0. Multiply through by the Least common denominator Getting rid of the fraction. These values go on # line! Fractional inequalities: You must test on the number line and see what interval works for your inequality. Sequences and series: Arithmetic – separated by a common difference. an a1 (n 1)d S Oh yeah, it’s on your formula sheet! Geometric- each term is multiplied by some number to get to the next one. Divide any term by the previous one to find r, the common ratio. an r an 1 an a1r Sum= n1 on your formula sheet! If you are given a recursive formula, plug in the first term to get the next term and then plug in that term to get the next one and so on……… an 2an1 1 Probability: r C ( p ) ( q ) n r nr At least r: r and up to n. At most r: r and down to 0. Probability: Use permutations when order is important. n Pr Use combinations when order is NOT important. C n r Probabilities based on Geometric figures are the ratio of areas. Area formulas: circle : a r 2 rectangle: a=bh Radical equations isolate the radical square both sides solve for x check your solutions Factoring: GCF Difference of squares Trinomial By grouping Absolute Value equations: isolate the abs. value set up two equations solve for x check your solutions Inequalities - # line! Functions: Vertical line test or no x’s repeat. one-to-one: no x’s or y’s repeat, horizontal and vert. line test. onto- all x’s and y’s are used, a line.