What are the minimum and the maximum values of (12sin X + 5cos X) respectively?

  1. 0 and 13
  2. -13 and 0
  3. -12 and 5
  4. -13 and 13

Answer (Detailed Solution Below)

Option 4 : -13 and 13
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Detailed Solution

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Given:

12sin X + 5cos X 

Concept Used:

Minimum value of a sinθ + b cosθ = -√(a2 + b2)

Maximum value of a sinθ + b cosθ = √(a2 + b2)

Calculation:

Minimum value of 12sin X + 5cos X  = -√(a2 + b2)

⇒ -√(122 + 52)

⇒ -13

Maximum value of 12sin X + 5cos X  = √(a2 + b2)

⇒ √(122 + 52)

⇒ 13

∴ The minimum and maximum value of 12sin X + 5cos X is -13 and 13 respectively. 

 

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