how to find out maximum and minimum value of trigonometric identities?

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Manoj Kumar Vishwakarma

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In case of sec2x, cosec2x, cot2x and tan2x, we cannot find the maximum value because they can have infinity as their maximum value. So in question containing these trigonometric identities, you will be asked to find the minimum values only. The typical question forms are listed below:
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mathematics only

Please, specify your problem because identities have max/min value 0 as sin^2+cos^2=1 ,i suppose your problem may be of type on which point ,so take derivative to 0 and then you can find max/min as usual in calculus we do, i hope it will help thanks and regards.
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Use first and second order differentials
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do you mean trignometric functions? not any different from normal ones - differentiate and equate to 0. see if the resulting trignometric equation can be solved. you may try other methods of simplifying the trignometric equation too to estimate the max/min.
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Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

to find out values, Maxima and Minima rule use first order derivative test and second order derivative test
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WELL EXPERIENCED TUTOR OF SCIENCE FROM 8TH TO M.Sc.

Min-Max table Min value Max value Can be written as sin ?, sin 2?, sin 9? …. sin n? -1 +1 -1 ? Sin n? ? 1 cos ?, cos 4? , cos 7? … cos n? -1 ? Cos n? ? 1 sin2 ? , sin2 4? , sin2 9? …sin2 n? 0 ...
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Min-Max table Min value Max value Can be written as sin ?, sin 2?, sin 9? …. sin n? -1 +1 -1 ? Sin n? ? 1 cos ?, cos 4? , cos 7? … cos n? -1 ? Cos n? ? 1 sin2 ? , sin2 4? , sin2 9? …sin2 n? 0 +1 Can be written as0 ? Sin2 n? ? 1 cos2 ? , cos2 3? , cos2 8? … cos2 n? 0 ? Cos2 n? ? 1 Sin ? Cos ? -1/2 +1/2 -1/2 ? Sin ? Cos ? ? ½ observe that in case of sin2? and cos2?, the minimum value if 0 and not (-1). Why does this happen? because (-1)2=+1 read less
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HOW TO FIND THE MAXIMUM AND MINIMUM VALUES OF A TRIGONOMETRIC IDENTITY We can find the maximum and the minimum value of any trigonometric identity with the help of second derivative test easily . Let me give you an easy example to clarify my point. Suppose we have to find the maximum and the minimum...
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HOW TO FIND THE MAXIMUM AND MINIMUM VALUES OF A TRIGONOMETRIC IDENTITY We can find the maximum and the minimum value of any trigonometric identity with the help of second derivative test easily . Let me give you an easy example to clarify my point. Suppose we have to find the maximum and the minimum values of sinx Let f(x)= sinx …………(1) Differentiating the equation (1) w.r.t x, we get f’(x) = cosx …………….(2) At maxima and minima of f(x) ; f’(x)=0 So cosx = 0 ? x = ?cos?^(-1)?0 ? x = ?/2 or x = 3?/2, 0 0, as we know that according to second derivative test at the minima the value of the second derivative of a function is always positive, f(x) has its minimum value at x = 3?/2 . So the minimum value of sinx = sin3?/2 = - 1 Hence -1 < sinx < 1 In the same way we can find the maximum and the minimum values of any trigonometric identity. read less
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IGCSE and IBDP Math Facilitator

http://www.sscexamtutor.com/2014/07/easiest-way-to-find-maximum-and-minimum.html?m=1
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Expert Mohana in stat/Mat

a(sin^2) ? +b(cos^2) ? 1st type : !) if a>b, the maximum value = a and the minimum value = b !) if a
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