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

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