finding an anglewhat is the x angle if 2sin2x+square root 2=0?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve 2*sin 2x + sqrt 2 = 0

2*sin 2x + sqrt 2 = 0

=> 2*sin 2x = -sqrt 2

=> sin 2x = -1/sqrt 2

2x = arc sin (-1/sqrt 2)

=> 2x = -45 and -135

x = -45/2 + n*180 and x = -135/2 + n*180

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll move the numer alone to the right side:

2sin 2x = -sqrt2

We'll divide by 2:

sin 2x = -sqrt2/2

2x = (-1)^k*arcsin (-sqrt2/2) + kpi

2x = -pi/4 + kpi

We'll divide by 2:

x = -pi/8 + kpi/2

All the angles x = -pi/8 + kpi/2, where k is an integer number, verify the equation 2sin2x+square root 2=0.

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