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Find the range of cos(2x) +3sinx? And you= cos 2x+3sinx?

Find the range of cos(2x) +3sinx? 
And you= cos 2x+3sinx? 
 
 

Grade:12th pass

3 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
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Aditya
13 Points
3 years ago
Range of cos2x = [-1,1].
Range of 3 sinx = 3×[-1,1] = [-3,3]
On addition minimum value = (-1-3) = -4
Maximum value obtained = (1+3) = 4.
       Range of cos2x + 3sinx = [ -4,4].
 
Sushant kumar
13 Points
2 years ago
Cos2x+3sinx=(1-2sin2x)+3sinx
-2(sin2x-3/2sinx-1/2)
 
Making the term a perfect square by some manipulations
 
-2[sin2x - 2x3/4sinx +(3/4)2 - (3/4)2-1/2]
 
Y=  -2{[sinx-3/4]2-17/16}
 
(Sinx-3/4)2€[0,∞]
-2[sinx-3/4]2€ (-∞,0]
-2(sinx-3/4)2-17/18€(-∞,-17/18]
 
 

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