Monday, July 22, 2019
Comparing Properties of Trig Functions Essay Example for Free
Comparing Properties of Trig Functions Essay The properties of the 6 trigonometric functions: 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 2Ãâ¬, and the amplitude is 1. They have no asymptotes. The domain of tangent is all real numbers except for Ãâ¬2+kÃâ¬. The range is all real numbers and the period is Ãâ¬. Tan has no amplitude and has asymptotes when x= Ãâ¬2+kÃâ¬. The domain of a secant function is all real numbers except for Ãâ¬2+kÃâ¬. The domain of a cosecant function is all real numbers except for kÃâ¬. The range of both is (-âËž.-1]U[1,âËž) and the period is 2Ãâ¬. Secant has asymptotes when x=Ãâ¬2+kÃâ¬. Cosecant has asymptotes when x=kÃâ¬. They have no amplitude. Cotangentââ¬â¢s domain is all real numbers except for kÃâ¬. The range is all real numbers and the period is Ãâ¬. It has no amplitude and has asymptotes when x=kÃâ¬. In an inverse function, the x coordinate, or the domain, and the y coordinate, the range, switch places. Since only one to one functions have inverses, we take the interval -Ãâ¬2 to Ãâ¬2, which contains all the possible values of the sine function. Now, the new domain is [-Ãâ¬2, Ãâ¬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 [-Ãâ¬2, Ãâ¬2]. For cosine, the interval [0,Ãâ¬] 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,Ãâ¬] as the range. For arctan (x), the interval (-Ãâ¬2, Ãâ¬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 (-Ãâ¬2, Ãâ¬2) as the range. As you can see, the properties of the six trig functions have many similarities and the inverse trig functionsââ¬â¢ domain and range can be obtained with the one to one property of inverse functionsÃ'Ž
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment