Question

The maximum value of 3cosX + 4sinX+5 is

Answer 1

Answer:

10

Step-by-step explanation:

Thanks for the query !!

Prerequisites:

• Maximum Value of a equation involving Sin and Cos can be found by using formula : √ ( a² + b² ). Here, a refers to coefficient of Sin function and b refers to coefficient of Cos function.

Query: Maximum value of 3 Cos x + 4 Sin x + 5

According to the question,

⇒ a = 4 and b = 3

Hence applying in the formula we get,

⇒ √ ( 3² + 4² ) = √ 25 = ± 5

Now we know that greatest value can be obtained only if we use positive value. Hence Substituting the maximum value of 3 Cos x + 4 Sin x we get,

⇒ 5 + 5 = 10

Hence the maximum possible value for 3 Cos x + 4 Sin x + 5 is 10.

Answer 2

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 .

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