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Trigonometric functions

5.1

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Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A particle starts at x = 0 and moves along the x-axis with velocity v(t) = 0.2 for time t ? 0. Where is the particle at t = 7? A) x = 0.2 B) x = 1.4 C) x = 0.27 D) x = 7 1) 2) A particle moves with velocity v(t) = 2t + 7 find the distance traveled between t = 1 and t = 5. A) 18 B) 52 C) 26 D) 9 2) 3) A particle moves with velocity v(t) = 2t + 3 find the distance traveled between t = 0 and t = 2. A) 13 B) 15 C) 10 D) 17 3) Use a finite approximation to estimate the area of the region enclosed between the graph of f and the x-axis for a ? x ? b. 4) f(x) = x2, a = 2, b = 6

Precalc midterm study guide part 2

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Name:______________________________ Date:_____________________________ Midterm Review (continued) 53. Solve the triangle ABC given a = 9, b= 7, c = 5. 54. Solve the triangle ABC given a = 7, b=6, measure of angle A=26.3?. 55. Find the area of a triangle with sides 13, 15, 18. 56. Sketch a graph of the following trigonometric functions using the standard trig viewing window. f(x) = csc x f(x) = cot x f(x) = tan x f(x) = sec x 57. Evaluate 8 7tan,8 3cos,8 5sin ??? , sin 165?. 58. P(-5,-12) is on the terminal side of an angle in standard position with measure ,? where 0

Math A Guide

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A-Level Maths Revision notes 2015 1 Contents Coordinate Geometry ........................................................................................................................... 3 Trigonometry ......................................................................................................................................... 5 Basic Algebra ......................................................................................................................................... 8 Advanced Algebra ............................................................................................................................... 10

Graphs and Graphing Utilities

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1.1 - Graphs and Graphing Utilities TI-82 There are several kinds of graphs that the TI-82 or TI-83 will do, but they are accessed from the same key. The [y=] key and the [2nd] [y=] or [StatPlot] key. The two major kinds of plots may cause confusion when mixed, so it is best to turn off all unnecessary plots before trying to graph an equation. To turn off all statistical plots, hit [StatPlot] and choose option 4 - PlotsOff. Hit enter to finish the command. To turn off a regular plot, one can either hit [Clear] while on an equation, or arrow to the left so that the cursor is on the equal sign, and press enter to toggle the display of that equation. Graphing Equations with the Calculator

2003 AP MC

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? ? ? ? ? ? ? ? ? ? ? ? ? ? M AREA - COMPLETE THIS AREA AT EVERY EXAMINATION. ~The AP"'ADVANCEDTo maintain lhe security 01 lhe exam and the vaftdily 01 my AP grade, I will allow no one other than myseff to see the multiple-ohoice queslicns and wiD seal the appropriate section when asked to do so. t will not discuss these questions .. .. College PLACEMENT PLACE AN AP ? NUMBER LABEL _ Board PROGRAM" Iwith anyone at any time after the completion of the multipl_ section. I em awam 01 and agree 10 the Program'. ~ policies and procecilJteS as outlined in the 2003 Buffetin for AP Stt.tdImts and Parents. OR WRITE YOUR AP NUMBER Answer Sheet for May 2003, Form 3ZBP HERE AT EVERY EXAMINATION. PAGE 1 ,...,. W Plintexamination name:.______________________

Precalculus Functions Anecdotes

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1. Identity Function-This is the only function thats acts on every real number by leaving it alone 2. Square Root Function-Put any positive number into your calculator. Take the square root. Then take the square root again, and so on. Eventually you will always get 1. 3. Squaring Function-The graph of this function, called a parabola, had a reflection property that is useful in making flashlights and satellite dishes. 4. Cubing Function-The origin is called a ?point of inflection? for this curve because the graph changes the curvature at the point. 5. Reciprocal Function-This curve, called a hyperbola, also has a reflection property that is useful in satellite dishes. 6. Natural Log Function-This function increases very slowly. If the x-axis and y-axis

Pre-Calculus Functions Chart

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Sheet1 Formula Name Domain Range Increasing Interval Decreasing Interval Maximum Minimum x-Intercept y-Intercept End-Behavior VA HA Symmetry Continuity 1a(Parent) f(x)=x Identity Function (-?,?) (-?,?) (-?,?) None None None (0,0) (0,0) y-->? None None Odd Continuous 1b f(x)=x-6 None (-?,?) (-?,?) (-?,?) None None None (6,0) (0,-6) y-->? None None Neither Continuous 1c f(x)=x+3 None (-?,?) (-?,?) (-?,?) None None None (-3,0) (0,3) y-->? None None Neither Continuous 1d f(x)=3x None (-?,?) (-?,?) (-?,?) None None None (0,0) (0,0) y-->? None None Neither Continuous 1e f(x)=-x None (-?,?) (-?,?) None (-?,?) None None (0,0) (0,0) y-->-? None None Neither Continuous 1f f(x)=-3x+6 None (-?,?) (-?,?) None (-?,?) None None (2,0) (0,6) y-->-? None None Neither Continuous 1g y=a(x-h) +k

Summary of Trig Inverse Function

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Trig Inverse Function Summary Function Meaning Domain Range Quadrants of Found on the (i.e., possible (i.e., possible the Unit Circle calculator by values for x) values for y) from Which Range Values Come j=sin!x y is the angle in the first or [-1, 1] [-nI2, n12] I and IV sin" (X) j=arcsin x fourth quadrant whose sine value is x j=cosir Y is the angle in the first or [-1, 1] [0, n] I and II cos-I(X) y=arccos x second quadrant whose cosine value is x j=tanix y is the angle in the first or (-00, (0) (-nl2, n12) I and IV tan" (X) y=arctanx fourth quadrant whose , tangent value is x

Trig formula sheet

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All Rights Reserved: http://regentsprep.org Algebra 2 ? Things to Remember! Exponents: 0 1x ? 1m m x x ? ? ?m n m nx x x ?? ?( )n m n mx x? m m n n x x x ?? n n n x x y y ? ? ?? ?? ? ( ) ?n n nxy x y? Complex Numbers: 1 i? ? ; 0a i a a? ? ? 2 1i ? ? 14 2 1i i? ? ? divide exponent by 4, use remainder, solve. ( ) conjugate ( )a bi a bi? ? 2 2( )( )a bi a bi a b? ? ? ? 2 2a bi a b? ? ? absolute value=magnitude Logarithms log yby x x b? ? ? ln logex x? natural log e = 2.71828? 10log logx x? common log Change of base formula: log log logb a a b
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