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Trigonometry> Find the number of points of intersection...

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

Kawal , 10 Years ago

Grade 11

1 Answers

Jitender Singh

Last Activity: 10 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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