NSX Posted February 10, 2003 Share Posted February 10, 2003 When someone says "A is inversely proportional to B, it means A=k/B", where k is some proportionality constant. Or 2 inverse is 1/2, or 0.5, or 2^-1 = 1/2. Why is that sin inverse, although written as sin^-1 is not 1/sin? Likewise for cosine and tangent. Link to comment Share on other sites More sharing options...
fafalone Posted February 10, 2003 Share Posted February 10, 2003 It's properly written arcsine. When you take the sine of a number, it gives you a decimal result. Arcsine takes a decimal result and turns it in to the angle measure. Link to comment Share on other sites More sharing options...
NSX Posted February 10, 2003 Author Share Posted February 10, 2003 Originally posted by fafalone It's properly written arcsine. When you take the sine of a number, it gives you a decimal result. Arcsine takes a decimal result and turns it in to the angle measure. Ah..so ie. sin(45) = 0.707106781..., this would be sine? AND arcsine (0.707106781...) = 45? Link to comment Share on other sites More sharing options...
blike Posted February 10, 2003 Share Posted February 10, 2003 Yes BUT that is not the only solution, 135 degrees would also be a solution [remember the unit circle], although I believe most calcs only give one solution. Link to comment Share on other sites More sharing options...
fafalone Posted February 10, 2003 Share Posted February 10, 2003 since arcsin is only defined for -1<x<1, there is only one possible value for arcsin for any number in that range. Link to comment Share on other sites More sharing options...
blike Posted February 10, 2003 Share Posted February 10, 2003 Ah, that would be why. I suppose its left to the student to calculate other solutions. Link to comment Share on other sites More sharing options...
fafalone Posted February 10, 2003 Share Posted February 10, 2003 there are no other solutions. multiple solutions for sine, not arcsine. Link to comment Share on other sites More sharing options...
blike Posted February 10, 2003 Share Posted February 10, 2003 There was a problem set in trig last semester that required us to use the inverse sine function to find an angle, then find the other angle using the angle provided by inverse sin. Link to comment Share on other sites More sharing options...
NSX Posted February 10, 2003 Author Share Posted February 10, 2003 Cool. Thanks guys! So is it called arctangent and arccosine for the tangent and cosine respectively? Link to comment Share on other sites More sharing options...
fafalone Posted February 10, 2003 Share Posted February 10, 2003 yeah. as well as arcsecant, arccosecant, arccotangent, etc Link to comment Share on other sites More sharing options...
NSX Posted February 10, 2003 Author Share Posted February 10, 2003 So what about functions like cosecant, secant, etc.? Do they have a inverse like opposites too? Link to comment Share on other sites More sharing options...
NSX Posted February 23, 2003 Author Share Posted February 23, 2003 :feedback: Link to comment Share on other sites More sharing options...
Dave Posted March 1, 2003 Share Posted March 1, 2003 Originally posted by NSX So what about functions like cosecant, secant, etc.? Do they have a inverse like opposites too? yeah, but they're fairly useless. e.g. if you have the equation: cosec(x) = 2 then it's pretty obvious that this is just the same as sin(x) = 1/2 and x = arcsin(1/2) = :pi:/6 so it's just another set of functions that don't really have too much use Link to comment Share on other sites More sharing options...
Dave Posted March 1, 2003 Share Posted March 1, 2003 oh, also, you can define arccosecant etc in terms of arcsin etc. say you have an equation: cosec(a) = b then a = arccsc(b) but also, 1/sin(a) = b then a = arcsin(1/b) but a = arccsc(b), so arcsin(1/b) = arccsc(b) you can do a similar thing for arcsecant and arccotangent, but it's all fairly useless Link to comment Share on other sites More sharing options...
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