Looking over textbook, I realize they never use cos^-4, for example. They only use sec ^ 4. Is it wrong or just better?
2006-12-26 13:18:49 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
hey mayank k, Thats what I was worried about. But remember, arccos = Cos ^-1 not cos ^-1 (notice the capital).
I dislike working with sec as it is easier to just deal with cos. For example, when integrating, if you have sin and sec, it's hard to get your head around. But if you have sin and cos, you know exactly what to do: kill the sin, add one to the exponent of cos.
2006-12-26 13:27:14 · update #1
bictor, I don't know what you are referring to when you say function and relation. Can you elaborate?
2006-12-27 08:04:27 · update #2
cos^-1 represents arccos by convention, so using negative exponents would lead to confusion. That's probably why they have sec in the first place.
The distinction between capitalized and lowercase is not as you described. Cos^-1 (Arccos) is the function, with its range restricted, while cos^-1 (arccos) is the relation.
2006-12-26 16:43:49 · answer #1 · answered by bictor717 3 · 0⤊ 0⤋
I think the issue is as you identified, how do you distinguish between a negative exponent and an inverse function. I use cos^-1 for the inverse and just write a fraction for 1/cos. If I ever see sec (probably used exactly to avoid writing cos to a negative exponent) I translate it immediately into a fraction. A proper way to write a negative exponent would be with parentheses: (cos(x))^(-4)......
2006-12-26 23:42:55 · answer #2 · answered by a_math_guy 5 · 0⤊ 0⤋
They're all equivalent. you're free to use cos^-4 all you like.
negative exponents are the same as saying (1/whateverexpression) with a positive exponent.
for example, 2^-2 is the same as 1/(2^2).
so, cos^-4 is the same as 1/(cos^4), and since sec is the same as 1/cos, cos^-4 = sec^4.
2006-12-26 21:23:27 · answer #3 · answered by John C 4 · 0⤊ 0⤋
I think cos^-1 is not the same as sec. This is known as arccos.
2006-12-26 21:23:32 · answer #4 · answered by Anonymous · 0⤊ 0⤋
it probably just depends if you want to work with negative exponents or not. but i guess it's easier to work with positive exponents.
since sec can also be written is 1/cos which is equal to cos^-1 , then people probably just work with secants in order to have "nice" positive numbers to start with.
2006-12-26 21:23:26 · answer #5 · answered by Anonymous · 1⤊ 0⤋
cos^-4=sec^4 They are both equally correct. I usually use cos because my calculator has cos but not sec.
2006-12-26 21:21:17 · answer #6 · answered by mu_do_in 3 · 1⤊ 0⤋