Grade 88 grade maths

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

Seema

10 Years agoGrade 8

1 Answer

arun

Approved Tutor Answer10 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.