Question

Maximum value of ( 7 sin θ + 11 cos θ ) is

Answer 1

Answer:

√170

Step-by-step explanation:

we know that the range of an expression of the type a sin θ+ b cos θ from -√(a²+b²) to √(a²+b²).

i.e, -√(a²+b²)≤ (a sin θ+ b cos θ) ≤ √(a²+b²)

therefore,the maximum value of 7 sin θ+11 cos θ would be √(7²+11²) = √170

some additional information:

proof of the above result:

a sin θ+b cos θ

√(a²+b²)× { a sin θ/√(a²+b²) + b cos θ/√(a²+b²)}

[now let us assume that a/√(a²+b²) = sin φ

then, b/√(a²+b²) becomes cos φ]

now the expression becomes,

√(a²+b²) { sin φ sin θ+ cos φ cos θ}

or,√(a²+b²) { sin (φ+θ) }

[we know that -1≤sin θ≤1.]

or, -√(a²+b²) ≤ sin (φ+θ) ≤ √(a²+b²)

[proved]