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Find the maximum value of 24sin@ + 7cos@ I know the method of root of (a^2 + b^2). But how can we do it logically by converting any of the fuctions? Thanks

Find the maximum value of
24sin@ + 7cos@
 
I know the method of root of (a^2 + b^2). But how can we do it logically by converting any of the fuctions?
Thanks

Grade:8

1 Answers

Vikas TU
14149 Points
7 years ago
let y = 24sin@ + 7cos@ ….................(1)
differentiate it w.r.t @ and equate it 0.

dy/d@ = 24cos@ + -7sin@ = 0
tan@ = 24/7 ==> sin@ = 24/25 ==> cos@ = 7/25

Now put sin@ and cos@ values in eqn. (1)
= 625/25
= 25 is the answer.

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