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

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

Grade:8

1 Answers

arun
123 Points
5 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.

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