Free Essay

Rutuja

In:

Submitted By rutujak
Words 427
Pages 2
The graphs of the sine and cosine functions Let's continue to use t as a variable angle. A good way for human beings to understand a function is to look at its graph. Let's start with the graph of sin t. Take the horizontal axis to be the t-axis (rather than the x-axis as usual), take the vertical axis to be the y-axis, and graph the equation y = sin t. It looks like this.

First, note that it is periodic of period 2. Geometrically, that means that if you take the curve and slide it 2 either left or right, then the curve falls back on itself. Second, note that the graph is within one unit of the t-axis. Not much else is obvious, except where it increases and decreases. For instance, sin t grows from 0 to /2 since the y-coordinate of the point B increases as the angle AOB increases from 0 to /2.

Next, let's look at the graph of cosine. Again, take the horizontal axis to be the t-axis, but now take the vertical axis to be the x-axis, and graph the equation x = cos t.

Note that it looks just like the graph of sin t except it's translated to the left by /2. That's because of the identity cos t = sin (/2 + t). Although we haven't come across this identity before, it easily follows from ones that we have seen: cos t = cos –t = sin (/2 – (–t)) = sin (/2 + t).
The graphs of the tangent and cotangent functions The graph of the tangent function has a vertical asymptote at x = /2. This is because the tangent approaches infinity as t approaches /2. (Actually, it approaches minus infinity as t approaches /2 from the right as you can see on the graph.

You can also see that tangent has period ; there are also vertical asymptotes every units to the left and right. Algebraically, this periodicity is expressed by tan (t + ) = tan t.

The graph for cotangent is very similar.

This similarity is simply because the cotangent of t is the tangent of the complementary angle – t.
The graphs of the secant and cosecant functions The secant is the reciprocal of the cosine, and as the cosine only takes values between –1 and 1, therefore the secant only takes values above 1 or below –1, as shown in the graph. Also secant has a period of 2.

As you would expect by now, the graph of the cosecant looks much like the graph of the secant

Similar Documents

Premium Essay

Dress Codes

...Rutuja Kharate #214 8th Grade U.S History 14 March 2016 Sexual Discrimination in Dress Codes "If you are sexualizing me, you are the problem (Boboltz).” Some may believe that Dress Codes are aimed to provide modesty and to prevent distraction. On the contrary others believe, the dress code does not avert distraction and is utterly sexist. Limiting expression of clothing, objectifying young women, and sexualizing women’s bodies, are only a few reasons why the Dress Code has proven to be sexist. Originally, clothing was worn to provide protection from the outside world. As stated in the Eyewitness Book Clothes, “‘Invention’ [clothing] was the need of early people to protect them against the climate, whether hot, cold, wet or dry” (Warne 6)....

Words: 882 - Pages: 4

Free Essay

Product Offering

...Product Offering Lally Keyshla De Jesús, Josué Ubiles & Ariana Román University of Phoenix MKT/571 - Marketing Prof. Magda Oquendo Santiago January 31, 2013 Product Offering Kalix is a swimwear production company base in Puerto Rico. This company specializes in swimwear and sportswear design, manufacturing and distribution. Kalix manufacture their products in a custom manner basically on demand, which means it can be in small or large amount orders all depend on the customer needs. Furthermore this company mayor steady income came from local boutiques and retailers. As a growing company Kalix want to expand for that reason company designers came with a new product they expect to launch in and outside of the United States. Kalix have an exclusive line of products called Purple Drop, Purple Drop swim wear is a local line with great acceptance in the island. Purple Drop also have they star product call “Sleek Koture” and because of the remarkable local sales and demand of this product, Kalix want to try it out of the united state. * “Sleek Koture” is what women commonly known as body Shapers but with a twist. “Body shapers are made out of strong materials (typically a mixture of nylon and lycra) that are able to force the body into shape and instantly make anyone seem inches thinner. All companies claim that their body shapers are comfortable, and they truthfully are more comfortable than the corset of the past” (Essorment, 2012). * We called it shaper...

Words: 1226 - Pages: 5

Premium Essay

Electronics

...idUNIVERSITY OF PUNE , RESULT SHEET FOR B.E.(2008 PAT.)(CIVIL) EXAMINATION NOV. 2013 DATE : 14 MAR. 2014 NOTE: FIRST LINE : SEAT NO., CENTRE : K.K. WAGH COLLEGE OF ENGINEERING, NASIK. NAME OF THE CANDIDATE, MAX. MARKS, MOTHER, PERMANENT REG. NO., MARKS OBTAINED, PREVIOUS SEAT NO., P/F:PASS/FAIL, PAGE NO. COLLEGE, 01 (1638) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEAT NO. OTHER LINES: HEAD OF PASSING, MAX.MARKS : 1500 B80130001 010 . ENVIRONMENTAL ENGINEERING II 010 . ENVIRONMENTAL ENGINEERING II 010 . ENVIRONMENTAL ENGINEERING II 020 . DAMS AND HYDRAULIC STRUCTURE 020 . DAMS AND HYDRAULIC STRUCTURE 020 . DAMS AND HYDRAULIC STRUCTURE 030 . STRUCTURAL DESIGN III 030 . STRUCTURAL DESIGN III 030 . STRUCTURAL DESIGN III 04B . SYSTEMS APPROACH IN CIVIL ENGG 04B . SYSTEMS APPROACH IN CIVIL ENGG 05E . ADVANCED CONCRETE TECHNOLOGY FIRST TERM TOTAL = B80130002 424/750. SUNITA PP TW OR PP TW OR PP TW OR PP TW PP 100 25 50 100 25 50 100 25 50 100 25 100 40 10 20 40 10 20 40 10 20 40 10 40 55 22 38 61 15 28 41 14 06 52 19 40 P P P P P P P P F P P P , 71104334F , , KKNS , MIN. PASS MARKS, C: PREVIOUS CARRY OVER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DISTINCTION : 0990 PP TW OR PP TW OR PP TW OR PP TW PP 100 25 50 100 25 50 100 25 50 100 25 100 40 10 20 40 10 20 40 10 20 40 10 40 FIRST CLASS : 900 MEENA 55...

Words: 138108 - Pages: 553