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Find the number of points of intersection of y = cosx & y = sin3x between -(pi)/2 & (pi)/2.

Find the number of points of intersection of 
y = cosx & y = sin3x between -(pi)/2 & (pi)/2.

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:Hello student, please find answer to your question
Two curves are intersecting, so
cosx = sin3x
cosx = cos(\frac{\pi }{2}-3x)
x = 2n\pi \pm (\frac{\pi }{2}-3x)
x\pm 3x = 2n\pi \pm \frac{\pi }{2}
4x = 2n\pi + \frac{\pi }{2}
n = 0
\Rightarrow x = \frac{\pi }{8}
n = -1
x = \frac{-3\pi }{8}
-2x = 2n\pi -\frac{\pi }{2}
n = 0
x = \frac{\pi }{4}
So there are three points of intersection.

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