Question

5sin theta+4 cos theta minimum value

Answer 1

2 + sin theta would be the answer i guess

Answer 2

Answer:

5sin theta+4 cos theta minimum value is - 6.40

Step-by-step explanation:

We know that,

The minimum and the maximum value of a sinθ + b cosθ is given as :

$-\sqrt{a^{2} +b^{2} }$ ≤  a sinθ + b cosθ ≤ $\sqrt{a^{2} +b^{2} }$

On comparing,

5 sinθ + 4 cos θ with a sinθ + b cosθ we get,

a  = 5

b = 4

Substituting the values of a and b in the equation we get,

$-\sqrt{5^{2} +4^{2} }$ ≤  5 sinθ + 4 cosθ ≤ $\sqrt{5^{2} +4^{2} }$

$-\sqrt{25 +16 }$ ≤  5 sinθ + 4 cosθ ≤ $\sqrt{25 +16 }$

$-\sqrt{41}$ ≤  5 sinθ + 4 cosθ ≤ $\sqrt{41}$

So,

Minimum of ( 5 sinθ + 4 cos θ ) = $-\sqrt{41}$ = - 6.40

Hence,

5sin theta+4 cos theta minimum value is - 6.40