Grade 12th passTrigonometry
Find the range of cos(2x) +3sinx? And you= cos 2x+3sinx?
Find the range of cos(2x) +3sinx?
And you= cos 2x+3sinx?
3 Answers
Saurabh Koranglekar
Aditya
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
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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