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Q: 5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

  • 1
    -13
  • 2
    11
  • 3
    13
  • 4
    -11
  • Show Answer
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Answer : 3. "13"
Explanation :

Answer: C) 13 Explanation: Given,  5sinx + 12cosx ≥ -r  ⇒13513sin x + 1213cos x ≥ -rcosx) ≥ -r  513= cosA => sinA =1213   => 13(sinx cosA + sinA cosx) ≥ -r   => 13(sin(x + A)) ≥ -r   we know that , -1 ≤ sin (angle) ≤ 1   => 13sin (x + A) ≥ -13 ⇒rmin =13

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