Question

find the greatest and least values f 4sin theta +3cos beta+7​

Answer 1

Given  

find the greatest and least values of 4 sin theta +3 cos theta+7

ANSWER

 Now we have 4 sin theta + 3 cos theta + 7  

 We know that  √4^2 + 3^2 = √16 + 9 = 5

 Now 5/5(4 sin theta + 3 cos theta ) + 7

   5 (4/5 sin theta + 3/5 cos theta) + 7

By Pythagorean triplet

let sin ∝ = 3/5 and cos ∝ = 4/5

Now 5(cos∝ sin theta + sin ∝ cos theta) + 7

    5 (sin (theta + ∝) + 7

 We can write this as

    5 < 5 sin (theta – ∝) < 5

  5 + 7 < 5 sin(theta – ∝)< 5 + 7

   2 < 5 sin (theta – ∝) < 12

 So minimum value is 2 and maximum value is 12