Question

Find the maximum and minimum values of
3 cosA + 4 sinA+5.
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Answer 1

Answer:

Find the maximum valus of 3cos+4 sinA+5

Step-by-step explanation:

Answer

10 is the maximum value !

Step-by-step explanation

Let f ( x ) = 3 cos x + 4 sin x + 5 .

We have to find the maximum value of the given function .

In order to find the maximum value follow these steps :

Formula for maximum value

When we are to find the maximum value of a sin x + b cos x :

Maximum value = √ ( a² + b² )

Minimum value = - √ ( a² + b² )

Find the maximum value of 3 sin x + 4 cos x

hence the maximum value of 3 sin x + 4 cos x

= > √ ( 3² + 4² )

= > √ ( 9 + 16 )

= > √ 25

= > ± 5

The maximum value will be 5.

Find the maximum value of the function .

3 sin x + 4 cos x will have maximum value of 5.

Hence adding 5 both sides :-

= > 3 sin x + 4 cos x = 10 for maximum value .

Hence the maximum value of the given question will be 10