Question

2sin²∅+3sin∅=-1

find ∅

Answer 1

Hey there !

2sin²∅+3sin∅=-1

2sin²∅+2sin∅+sin∅+1=0

2sin∅(1+sin∅)+1(1+sin∅)=0

2sin∅+1(1+sin∅)=0

2sin∅+1=0

sin∅=-1/2

sin∅=sin(-30)

1+sin∅=0

sin∅=-1

∅=-30,-90,270,330

Answer 2

Heya

Here is your answer

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2sin²∅ + 3sin∅ = -1

=> 2sin²∅ + 3sin∅ + 1 = 0

=> 2sin²∅ + 2sin∅ + sin∅ + 1 = 0

=> 2sin∅ ( sin∅ + 1 ) + 1 ( sin∅ + 1 ) = 0

=> ( 2sin∅ + 1 ) ( sin∅ + 1 ) = 0

Either

2sin∅ + 1 = 0 or sin∅ + 1 = 0

=> sin∅ = -1/2 or sin∅ = - 1

=> sin∅ = - sin30

=> sin∅ = sin ( 180 + 30 ) or sin( 360 - 30 )

= sin210 or sin330

.°. ∅ = 210, 330

Again,

sin∅ + 1 = 0

=> sin∅ = - 1

=> sin∅ = - sin90

=> sin∅ = sin( 180 + 90 ) or sin( 360 - 90 )

= sin270 or sin 270


.°. ∅ = 210 , 270, 330

thanks

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