Integration using trig identities or a trig substitution some integrals involving trigonometric functions can be evaluated by using the trigonometric identities. Jun 01, 2014 provides examples of trigonometric graph transformations for gcse. See what a vertical translation, horizontal translation, and a reflection behaves in three separate examples. Coterminal angles related acute angles finding all possible measures of an angle using raa, cast, and coterminal angles0 trig ratios of any angle special triangles finding exact values modelling periodic behavior sketching trig functions transformations of periodic functions trig. Trig cheat sheet definition of the trig functions right triangle definition for this definition we assume that 0 2 p of the trig functions will be addressed later. Unit 2a graphing trig functions selfassessment and tracker in this unit i. This section requires the unit circle and table from last section. Transforming the graphs of trigonometry functions dummies.
Trigonometric functions practice test radian measure. This study aid is intended for students of physical and mathematical faculties of pedagogical institutes. Graphing trig functions day 1 find the period, domain and range of each function. An investigation of functions 2nd ed david lippman and melonie rasmussen. Transformation of trigonometric graphs solutions, examples. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear. Many of these functions can be identi ed by their \shape, by general. In this unit we examine these functions and their graphs. An investigation of functions is a free, open textbook covering a twoquarter precalculus sequence including trigonometry. Chapter 11 434 chapter table of contents 111 graph of the sine function 112 graph of the cosine function 1 amplitude,period,and phase shift 114 writing the equation of a sine or cosine graph 115 graph of the tangent function 116 graphs of the reciprocal functions 117 graphs of inverse trigonometric functions 118 sketching trigonometric graphs chapter summary. You will probably be asked to sketch one complete cycle for each graph, label significant points, and list the domain, range, period and amplitude for each graph. Transformations of trigonometric graphs matchup teaching.
Most of the problems will give key insights into new ideas and. Graphical transformations of functions in this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. We can easily get a qualitatively correct idea of the graphs of the trigonometric functions from the unit circle diagram. Which of the following radian measures is the largest. Graph and list amplitude, period, phase shift, vertical shift and xaxis flip for each of the following. The range is all possible values to get out of the function. The letter a represents the amplitude of the sine or cosine function, and it affects the steepness or flatness of the graphs of any of the trig functions. Match the following graphs to the equations at the bottom. Amplitude a period or horizontal shift c vertical shift d steps to sketch 1. Introduction to trigonometric functions the university of sydney.
Find the general equation of the asymptotes and two specific asymptotes on all sec,csc, tan, and cot functions. Convert all trig functions in the integrand into products of sine and cosine. Transformations of trig functions mechanical engineering. Smith shsu elementary functions 20 5 35 vertical shifts lets graph these all on one plane to show the e ect of the shifting. Exact values for trigonometric functions of most commonly used angles. Integration using trig identities or a trig substitution. Revision summary gcse trig graph transformations teaching. Trigonometry lecture notes and exercises by daniel raies. It does not include fx notation as this was aimed at a higher tier lower ability group. The sine and cosine functions take on values between 1 and 1. Trig functions right triangle and unit circle definitions domain, range, and period. A periodic function has regular repetitive behavior.
Summary of trig integration we now know the following facts about trig functions and calculus. Trigonometric functions by daria eiteneer topics covered. Trig cheat sheet definition of the trig functions right triangle definition for this definition we assume that 0 2 p oct 28, 2014. In this post, we will see the book solving problems in algebra and trigonometry v. Graphs of the trigonometric functions sine, cosine and tangent, together with some tabulated values are shown here for reference. We also see how to restrict the domain of each function in. Vertical translations a shift may be referred to as a translation. Here are some examples, first with the sin function, and then the cos the rest of the trig functions will be addressed later. In the previous example, it was the factor of cosx which made the substitution possible. Elementary functions function transformations part 1, functions. For trig functions there are some important quantities that give us information about the shape of the graphs, and we should figure out how the various. You can print one from the website underneath the video exact values. Trigonometry notes for an entire trig course in pdf form. It is not only in trigonometric functions, all functions fall under this notation.
Definitions of trigonometric functions for a right triangle. Periods of other general trig functions y csc bx y sec bx y cot bx ex cot x y3inx 2tl regular period new period regular period of y csc x is 27t 27t 2tc csc 4x a. Feb 23, 2014 use these three sets of matching cards to get your students thinking about how the graphs of y sinx, y cosx and y tanx are transformed under single transformations good revision of c1 concept. Graphs of the trigonometric functions conic sections circles parabolas focus o, p, directria y ellipses hyperbolas foci p y csc sine and cosine curves y a b o one f. Here is a set of practice problems to accompany the transformations section of the common graphs chapter of the notes for paul dawkins algebra course at lamar university. We define the amplitude to be onehalf of the difference of the greatest value the function and the least value of the function. Inverse trig functions comprehensive summary of trig formulas and graphs. Trigonometric functions so far we have used only algebraic functions as examples when. Here is a simple strategy that is useful for solving a wide range of integrals involving trig functions.
It is suitable for a onesemester course at the college level, though it could also be used in high schools. Each of the numbers changes the basic graph in a particular way. The vertical displacement by d units and phase shift by c units do not change the shape of a function, so they also do not affect the period of the function. A ball in a pinball machine moves 1 3 of the way through a circular groove that has radius 3 m. By scaling vertically either function by a factor of a, the values of the function lie between a and a. The period of the sine, cosine, and tangent functions are only dependant on the horizontal stretch, b. Elementary functions function transformations part 1. Trigonometric functions, acute angles and right angles, radian measure and circular functions, graphs of the trigonometric functions, trigonometric identities, inverse trig functions and trig equations, applications of trigonometry and. Transformations of trig functions we can do all the usual tranformations to the graphs of the trig functions. Solution because the graph is a transformation of the graph of y 2cos 2 3 x, the amplitude is 2 and the period is 3by comparing the given equation to the general equation. Here are the abcs of reading the general equation for a trig function. Find the period of y find the period of y cot x new period of y csc 4x is regular period of y. From our trigonometric identities, we can show that d dx sinx cosx. Contents iii 8 inverse trigonometric functions 64 8.
Familiarity with the graphs of these functions is essential. The prerequisites are high school algebra and geometry. Trigonometric functions, acute angles and right angles, radian measure and circular functions, graphs of the trigonometric functions, trigonometric identities, inverse trig functions and trig equations, applications of trigonometry and vectors. You have probably met the trigonometric ratios cosine, sine, and tangent in a right angled triangle, and have used them to calculate the sides and angles of those. Graph trig functions sine, cosine, and tangent with all of the transformations the videos explained how to the amplitude and period changes and what numbers in the equations. Transformations of trig functions a linear combination of sine and cosine with the same argument can be expressed as a single trig function with an amplitude and phase. These allow the integrand to be written in an alternative form which may be more amenable to integration. Under its simplest definition, a trigonometric lit.