Find the minimum value of expression 7sin θ + 8cos θ?

  1. √87
  2. -√113
  3. √129
  4. -√15

Answer (Detailed Solution Below)

Option 2 : -√113
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Detailed Solution

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Given:

A trigonometric expression 7sin θ + 8cos θ is given

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

Minimum value for expression a sin θ + b cos θ = -√(a2 + b2)

Calculation:

The expression is 7 sin θ + 8cos θ

Now, by comparing the given expression with the standard expression the value of a and b are

∴ a = 7 and b = 8

∴ Minimum value = -√{(7)2 + (8)2}= -√113

Hence, option (2) is correct

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