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Question
Range of function f(x) = cos(ksinx) is [ -1,1], then the least positive integral value of k will be?
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Solution
Given f(x) = cos(KSinx) Now: range of this function is given as full range of cosx function (-1 to 1)Now assuming you meant it includes - 1 to 1 as well, then basically cosx ranges from -1 to 1 if X comes from 0 to Pi or 0 to 3.14159 approximately. So now we know KSinx should come from 0 to 3.14159 (approximately) .Range of Sinx is -1 to +1..so if we have to multiply by some natural number K to make it extend itself to 3.14159 that K must be greater than 4. Hence K >= 4 (it can be greater also as Cos is periodic.. Even from 2pi to 3pi it attains - 1 to 1 value.. I.e from 6.28 to 9.42 approximately
Given f(x) = cos(KSinx) Now: range of this function is given as full range of cosx function (-1 to 1)Now assuming you meant it includes - 1 to 1 as well, then basically cosx ranges from -1 to 1 if X comes from 0 to Pi or 0 to 3.14159 approximately. So now we know KSinx should come from 0 to 3.14159 (approximately) .Range of Sinx is -1 to +1..so if we have to multiply by some natural number K to make it extend itself to 3.14159 that K must be greater than 4. Hence K >= 4 (it can be greater also as Cos is periodic.. Even from 2pi to 3pi it attains - 1 to 1 value.. I.e from 6.28 to 9.42 approximately
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