# Can you please guide me in calculating  maximum and minimum of trigonometric equations. Say,Sin^2@ + cos^4@Thanks.

arun
123 Points
6 years ago
you can use two ways one is maxima and minima, in which you differentiate the function and put it equal to 0 and find the value for which the function will have a maximum or minimum value subsituting it in the function you will get your answer.
another method is to simplifying it in such a way that there exist only one type of trigonometric function like your question in this
$\sin^2x +\cos^4x = 1-\cos^2x +\cos^4x$
$\Rightarrow \sin^2x +\cos^4x = 1-\cos^2x(1-\cos^2x)$
$\Rightarrow \sin^2x +\cos^4x = 1-\cos^2x(\sin^2x)$
$\Rightarrow \sin^2x +\cos^4x = 1-\frac{1}{4}(4\sin^2x\cos^2x)$
$\Rightarrow \sin^2x +\cos^4x = 1-\frac{1}{4}(\sin^22x)$
substituting the maximum and minimum value of sin22x which are 1 and 0 respectively you will get the minimum and maximum values of function for respective values.