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If cot x = 2 / 3 and x is in quadrant 4, find: sin(x / 2)
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If cot x = 2 / 3 and x is in quadrant 4, find: sin(x / 2)
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Nov 28, 2017
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If cot x = 2 / 3 and x is in quadrant 4, find:
sin(x / 2)
Mathematics
high-school
Buford
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Buford
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Cot = adjacent / opposite = 2/3 but it lies in the 4th quadrant so 2/-3
Sin = opposite / hypotenuse , you have it as x/2
So you have the hypotenuse and the opposite is -3 so -3/2
Sin(-3/2) = -sin (3/2)
Alternative form : -0.997495
Bleeding Fingers
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Dec 1, 2017
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Bleeding Fingers
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cos x / sin x = 2 / 3
2 sin x = 3 cos x
sin x = 3 cos x / 2
sin² x + cos² x = 1
9 cos² x / 4 + cos² x = 1 / * 4
9 cos² x + 4 cos² x = 4
13 cos² x = 4
cos x = 2 / √13
sin ( x/2 ) = √ [( 1 - cos x )/ 2] = √ [( 1 - 2/√13 ) / 2] =
√(√13 - 2 )/(2√13)
or
sin ( x/2 ) ≈ 0.471858
Loilo
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Dec 2, 2017
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Loilo
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