What is Trig functions: Definition and 218 Discussions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane from which some isolated points are removed.
i have a problem graphing trig functions such as f(x) = 2cos(3x+pi/2) -1
i know this should be very simple but i am missing something :frown:
can someone explain the way youd go about graphing this
amp= 2
period = 2pi/3
y trans = -1
x trans = (pi/2)/3 [right?]
so when i try...
Hello everyone,
I am having some trouble finding the integral of tanxsec^2x. I honestly have no idea where to go with this one. I've finished all the others but this one is really screwing me up. I tried doing something with the chain rule but it didn't work out at all. I know that I am...
Hello all. I missed a class in calculus so I didn't get the notes on this so if anyone could explain this question for me, it would be much appreciated.
\lim_{x \rightarrow 0} \frac {tanx}{4x}
= \frac {sinx}{cos4x} ?
Not really too sure if I manipulated the equation right. Any hints...
I am taking calculus and math 12 at the same time. Now we are doing limits of trigonometric functions, but i know nothing about it. What are some important trig functions that i have to memorize?
Ex. I have no idea how to do these
lim (tanx-sinx)/xcosx
x->0
How does a calculator approximate a trig function. For example, you punch in sin(37deg) and the calculator will give you 0.6018150232. how does it figure this out?
My question is to determine the values of the primary and secondary tri functions at (-3,-4) on the terminal arm of an angle theta in standard position
Im just wondering how do u know which quadrant this point is in? I have assumed it is in quadrant 1. Then that means x=-3, y=-4, and r=5...
I believe that calculators use Taylor expansions to compute sines, cosines and tan's based upon the argument \theta (in radians of course). However, my question is, aside from these expansions, is there some sort of link between \theta and the output of the function itself.
I mean I know that...
I've been thought trig functions in school definitely, but never been told how were they invented in the first place! Also, is there a function like sin (theta)= something. If so, what are these functions?
however stupid it sounds, I don't know how to evaluate trig functions with my calculator... ex.
d(t) =0.5cos2t
how do i solve for t (lets say t is 2). Thanks in advance.
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...
I'm a bit confused at the moment. All my books say that normal and inverse trig.functions cancel each other out like this
\sin(\arcsin(x))=x and \arcsin(sin(x))=x
But when I try this out on my calculator - TI-89 - it only wants to recognize the first equation as being equal to x. Is that...
Guys, I am in Calculus 2, but I still have trouble seeing the answer when u plug in a radian measure into a trig function. My teacher assumes we know the answer right away. I know Sin(0)= 0 and Cos(0)=1, but that's about it.
I don't know things like Sin(pi/2) I have to input it into the...
srry to be a bother but can someone help me on how to do this, it explains it in the book but i don't understand.
Here it is:
arcsin(sin 3(pi))
i would really appreciate ur help, and thxs before hand. :smile:
Supposing I need to solve a problem like: sec(arctan 2) or cos(2arcsin(5/13)), is there a method I could use that would not require a calculator? What I mean is that for an example like tan(arccos .5), the answer is "simple" because I know the arc cosine of .5 is pi/3 and then the tan of pi/3 is...
I am having trouble with the following problems:
1) lim as x -> 0 of (sin 3x)/2x
2) lim as x -> 0 of (tan 5x)/(sin 2x)
3) lim as x -> 0 of (sin²3x)/2x
4) lim as h -> 0 of [(h+x)³ -x³]/h
5) lim as h -> 0 of [1/(x+h) - 1/x]/h
*Thanks for your help
How do I go about integrating
sin[y*sin(x)]*sin(x) wrt x from -pi to pi,
I've got that its an even function so I can change the limits to 0 to pi and double it, but I can't find the analytic answer. By parts? substitution? although for substitution I assume there needs to be a cos...
I am currently learning how to simplify trig functions, but is there a way to know which formulae to use?
In my textbook there are three formulae:
cos^2ttheta + sin^2theta = 1
1 + tan^2theta = sec^2theta
cot^2theta + 1 = cosec^2theta
I am also stuck in this question:
prove this...