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Find the maximum and minimum value of 9 CosA + 40 SinA + 40

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Find the maximum and minimum value of 9 CosA + 40 SinA + 40
1). 89, -4
2). 85, -7
3). 87, -5
4). 81, -1


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Answered by on | Votes 2 |

⇒ Always look out for Pythagoras theorem, we know that (9, 41, 40) is one

⇒ ∴ 41 (9/41 CosA + 40/41 SinA)

⇒ Let there be an angle B for which SinB = 9/41, CosB = 40/41

⇒ 41 (SinB CosA + CosB SinA) + 40

⇒ 41 (Sin(A + B)) + 40

⇒ We know that Sin(A + B)max = 1

⇒ Max value = 41 × 1 + 40 = 81

⇒ Min value = 41 × (-1) + 40 = -1

∴ Answer is -1

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