Question
If 3sinx + 4cosx + r is always greater than or equal to 0, what is the smallest value that r can take?
Answer: Option A
:
A
3 sinx +4 cosx + r ≥ 0
3 sinx + 4 cosx ≥ -r
5×(35sinx+45cosx)≥−r
Let 35 = cos A ⇒ sin A ⇒45
5(sin x cos A +sin Acos X)≥ -r
5(sin(X+A))≥ -r
We have -1 ≤ sin (angle) ≤ 1
5 sin(X+A)≥ -5
rmin =5.
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:
A
3 sinx +4 cosx + r ≥ 0
3 sinx + 4 cosx ≥ -r
5×(35sinx+45cosx)≥−r
Let 35 = cos A ⇒ sin A ⇒45
5(sin x cos A +sin Acos X)≥ -r
5(sin(X+A))≥ -r
We have -1 ≤ sin (angle) ≤ 1
5 sin(X+A)≥ -5
rmin =5.
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