Comparing Properties of Trig Functions Essay Example for Free

Comparing Properties of Trig Functions EssayThe properties of the 6 clean-cutonometric functions sin (x), cos (x), tan(x), cribbage (x), sec (x) and csc (x) include the firmament, set about, period, asymptotes and amplitudes. The domain of a cosine and sine function is all real numbers and the ramble is -1 to 1. The period is 2, and the amplitude is 1. They micturate no asymptotes. The domain of tangent is all real numbers except for 2+k. The range is all real numbers and the period is . burning has no amplitude and has asymptotes when x= 2+k. The domain of a secant function is all real numbers except for 2+k. The domain of a cosecant function is all real numbers except for k. The range of both is (-.-1U1,) and the period is 2. Secant has asymptotes when x=2+k. Cosecant has asymptotes when x=k. They have no amplitude. Cotangents domain is all real numbers except for k. The range is all real numbers and the period is . It has no amplitude and has asymptotes when x=k.In an in verse function, the x coordinate, or the domain, and the y coordinate, the range, spank places. Since only one to one functions have inverses, we take the interval -2 to 2, which contains all the possible values of the sine function. Now, the new domain is -2, 2, while the range stays the same. We then switch the domain and the range, so the domain and range of arcsin (x) is -1,1 and -2, 2. For cosine, the interval 0, contains all possible values, and the range is still -1,1. To find arcos (x) we invert the domain and range again, to get -1,1 as the domain and 0, as the range. For arctan (x), the interval (-2, 2) includes all possible values. The range still remains all real numbers. Exchanging the domain and range gives us all real numbers as the domain and (-2, 2) as the range.As you can see, the properties of the six trig functions have many similarities and the inverse trig functions domain and range can be obtained with the one to one property of inverse functions