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Solvig hw 17

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Solvig hw 17

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Step 1

To find all the values of x satisfying the given equation , with x in the interval [0,2pi)

Step 2

Using the standard identity, reduce the equation to a quadratic equation in cosx

2sin2 x-cosx1= 0, x E [0,27)
Use the identity: sin x+ cos x=1
or, sin 1-cos'x,to obtain
21-cos x)cosx-1= 0
2cos2 xcos1 0,
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2sin2 x-cosx1= 0, x E [0,27) Use the identity: sin x+ cos x=1 or, sin 1-cos'x,to obtain 21-cos x)cosx-1= 0 2cos2 xcos1 0,

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Step 3

Factorize the quadratic equation and solve for cos x,  and henc...

2cos2 xco-1=0,
+
(2cosx-cosx+ 1) = 0
cos.x-1,withx [0,27)
so, cos x
57
so.x
3 3
help_outline

Image Transcriptionclose

2cos2 xco-1=0, + (2cosx-cosx+ 1) = 0 cos.x-1,withx [0,27) so, cos x 57 so.x 3 3

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