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Chandan Das Grade: Upto college level
```        1.Find the range of 3sinx+4cosx-5.
2.If [2sinx]+[cosx]=-3,then the range of the fnctn f(x)=sinx+√3cosx in [0,2Π]is;(whr [.] denotes GIF).```
7 years ago

Ramesh V
70 Points
```										(1)
3sin(x) - 4cos(x) = 5 sin(x + arcsin(-4/5))
Thus,  the range of the function asin x - bcos x is ± √[(a)^2 + (b)^2]
so here its : ±5 -5
whihc is [-10,0]
(2  ) given  [2sinx]+[cosx]=-3
so both sin x  and cos x lies on (-0.5 , -1]
it can be written as : 2 sin  (x+pi/3)
in (o,2pi ) sin (x+pi/3) range is [0.866,-1]
so its  range is [1.732, -2]
--
regards
Ramesh
```
7 years ago
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