Question

What is the minimum value of 3 sinx+4 cosx ?

Answer 1

Answer:

-5

Step-by-step explanation:

For calculating the maximum and minimum value of a trigonometric equation we can use this formula.

Condition: The Equation must be of the form: a Cos x + b Sin x.

Formula:

• Maximum Value = √ ( a² + b² )
• Minimum Value = - √ ( a² + b² )

In our Case, it is of the form:

⇒ 3 Sin x + 4 Cos x

Therefore, a = 4 and b = 3

⇒ Minimum Value = - ( √ 3² + 4² )

⇒ Minimum Value = - ( √ 25 ) = - ( 5 )

Hence the minimum value of the function is -5.

Have a great day !!

Answer 2

$\Rightarrow$ ANSWER :-

For calculating the maximum and minimum value of a trigonometric equation we can use this formula.

Condition: The Equation must be of the form: a Cos x + b Sin x.

Formula:

Maximum Value = √ ( a² + b² )

Minimum Value = - √ ( a² + b² )

In our Case, it is of the form:

⇒ 3 Sin x + 4 Cos x

Therefore, a = 4 and b = 3

⇒ Minimum Value = - ( √ 3² + 4² )

⇒ Minimum Value = - ( √ 25 ) = - ( 5 )

Hence the minimum value of the function is -5.

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