Properties of Trigonometric Functions
The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x)are discussed. These include the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points. Sine Function: f(x) = sin (x)

* Graph

* Domain: all real numbers
* Range: [-1 , 1]
* Period = 2pi
* x-intercepts: x = k pi , where k is an integer.
* y-intercepts: y = 0
* Maximum points: (pi/2 + 2 k pi , 1) , where k is an integer. * Minimum points: (3pi/2 + 2 k pi , -1) , where k is an integer. * Symmetry: since sin(-x) = - sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the origin (0 , 0). * Intervals of increase/decrease: over one period and from 0 to 2pi, sin (x) is increasing on the intervals (0, pi/2) and (3pi/2 , 2pi), and decreasing on the interval (pi/2 , 3pi/2). Cosine Function : f(x) = cos (x)

* Graph

* Domain: all real numbers
* Range: [-1 , 1]
* Period = 2pi
* x intercepts: x = pi/2 + k pi , where k is an integer. * y intercepts: y = 1
* maximum points: (2 k pi , 1) , where k is an integer.
* minimum points: (pi + 2 k pi , -1) , where k is an integer. * symmetry: since cos(-x) = cos (x) then cos (x) is an even function and its graph is symmetric with respect to the y axis. * intervals of increase/decrease: over one period and from 0 to 2pi, cos (x) is decreasing on (0 , pi) increasing on (pi , 2pi).

Tangent Function : f(x) = tan (x)
* Graph

* Domain: all real numbers except pi/2 + k pi, k is an integer. * Range: all real numbers
* Period = pi
* x intercepts: x = k pi , where k is an integer.
* y intercepts: y = 0
* symmetry: since tan(-x) = - tan(x) then tan (x) is an odd function and its graph is symmetric with respect the origin. * intervals of increase/decrease: over one period and from -pi/2 to pi/2, tan (x) is increasing....

...Section 5.2 TrigonometricFunctions of Real Numbers
The TrigonometricFunctions
EXAMPLE: Use the Table below to ﬁnd the sixtrigonometricfunctions of each given real number t. π π (a) t = (b) t = 3 2
1
EXAMPLE: Use the Table below to ﬁnd the sixtrigonometricfunctions of each given real number t. π π (a) t = (b) t = 3 2 Solution: (a) From the...

...that occur in the natural world an in real life situation. A keen aptitude for math improves critical thinking and promotes problem-solving abilities. One specific area of mathematical and geometrical reasoning is trigonometry which studies the properties of triangles. In some of the fields such as architecture, astronomy , biology, cartography, chemistry, civil engineering, computer graphics, geophysics, crystallography and economics , some things in these fields cannot be...

...
PROPERTIES OF SINE AND COSINE FUNCTIONS:
1. The sine and cosine functions are both periodic with period 2π.
2. The sine function is odd function since it’s graph is symmetric with respect to the origin, while the cosine function is an even function since it’s graph is symmetric with respect to y axis.
3. The sine functions:
a. Increasing in the intervals[0, π/2]and...

...Trig Functions
Right triangle definition For this definition we assume that p 0 < q < or 0° < q < 90° . 2 Unit circle definition For this definition q is any angle.
y
( x, y )
hypotenuse opposite
y 1 x
q
x
q
adjacent sin q = opposite hypotenuse adjacent cos q = hypotenuse opposite tan q = adjacent hypotenuse opposite hypotenuse sec q = adjacent adjacent cot q = opposite csc q = sin q = y =y 1 x cos q = = x 1 y tan q = x 1 y 1 sec q = x x cot q = y csc q =
Facts...

...Trigonometric Identities
I. Pythagorean Identities
A. [pic]
B. [pic]
C. [pic]
II. Sum and Difference of Angles Identities
A. [pic]
B. [pic]
C. [pic]
D. [pic]
E. [pic]
F. [pic]
III. Double Angle Identities
A. [pic]
B. [pic]
=[pic]
=[pic]
C. [pic]
IV. Half Angle Identities
A. [pic]
B. [pic]
C. [pic]
6-1 Inverse Trig Functions p. 468: 1-31 odd
I....

...The properties of the 6 trigonometricfunctions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) include the domain, range, period, asymptotes and amplitudes.
The domain of a cosine and sine function is all real numbers and the range is -1 to 1. The period is 2π, and the amplitude is 1. They have no asymptotes. The domain of tangent is all real numbers except for π2+kπ. The range is all real numbers and the period is π. Tan has...

...Ashley Washington
Final exam essay
6/2/14
SixTrigonometricfunctions
The sixtrigonometricfunctions are found in a right triangle because they contain a right angle. The measures of the three angles, labeled A, B, and C. we used lower case letters a, b, and c to denote the lengths of the sides opposite of angles A, B, and C respectively. These sixtrigonometric...

...CIRCULAR FUNCTIONS AND TRIGONOMETRY
CONTENTS
-Angles and Their Measures
-Degrees and Radians
-Angles in Standard Position and Coterminal Angles
-Angles in a Quadrant
-The Unit Circle
-Coordinates of Points on the Unit Circle
-The Sine and Cosine Function
-Values of Sine and Cosine Functions
-Graphs of Sine and Cosine Functions
-The Tangent Function
-Graph of Tangent Function...

1237 Words |
5 Pages

Share this Document

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":35990992,"categoryName":"Literature","categoryParentId":null,"currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":3,"pageRange":"1-3","totalPages":3}},"access":"premium","title":"Properties of the Six Trigonometric Functions","additionalIds":[],"additional":[],"loadedPages":{"html":[],"text":[1,2,3]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Properties-Of-The-Six-Trigonometric-Functions-1072464.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.8","language":"en_US"},"analytics":{"googleId":"UA-32718321-1"}}