Simplifying Trig Functions: Understanding (a)(sin/cos/tan/cot/sec/csc) Graphs

[Kimorto]

can sumone think of an easier way to graph trig functions in the forms
(a)(sin(bx-c)
(a)(cos(bx-c)
(a)(tan(bx-c)
(a)(cot(bx-c)
(a)(sec(bx-c)
(a)(csc(bx-c)

I was wondering if sumone could explain what each part represents, like what does (a) does if i increase it, decrease it, make it negative, what b and c represent (i mean represent on the graph, does it stretch it shrink it, flip it make curves. I've missed a few days of school so i couldn't get the notes. Id also like to know how big the periods should be, how do i find asymtotes, range, domain. Anything to help me understand it would help greatly.

 

[Kimorto]

Someone help me

Someone help me grasp a better concept of graphing trig functions

 

[Nylex]

The a will increase the amplitude of the waves (actually, I'm not sure about tan, cosec, sec and cot). +/- c shifts the wave along the x-axis; + c shifts the function to the left and - c will shift the function to the right. b stretches the function, IIRC. The periods are how long it takes to go through one complete cycle (and then back to its starting position) of the function. For example, sin and cos have period 2π. Asymptotes are found by finding the points at which x and y tend to infinity. Eg. for tan, there's a vertical asymptote at π/2, as tan π/2 = 1/0. HTH.

 

[Integral]

In this day and age of spreadsheets and graphing calculators I simply do not understand why you bother asking such a question. My advise is to sit down with your calculator manual or a spreadsheet and start figuring out how to plot these functions. A picture is worth a 1000 words. It is trivial to set up a spreadsheet to graph those functions. In the blink of an eye you can change a parameter and see the effects. If you are incapable of using such hi tech tools then create a table of values and plot the points by hand. It will take a bit of time, but it may be time better spent then surfing the web looking for a free, thought free, answer.

 

[Kimorto]

cant use the technology

we have to be able to all this stuff with nothing but paper, pencil and basic mathmatical calculators I am in high school but I am takin gifted precal and that's why. Thanx for yalls help i easily understand cos and sin now. I just need help makin the other part into lamens terms.