if sin alpha=-3/5 where π<alpha<3π\2 then cos 1/2 alpha is
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If sin(a) = -3/5 , where a lies between pi <a < 3pi/2 , then cos ... if π < a < 3π/2 then π/2 < a/2 < 3π/4.
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sin^2(theta) + cos^2(theta) = 1
=> (-3/5)^2 + cos^2(theta) = 1
=> 9/25 + cos^2(theta) = 1
=> cos^2(theta) = 1 - 9/25
=> cos^2(theta) = 16/25
=> cos(theta) = +/- 4/5
However, it is given that theta is between π and 3π/2, so this puts theta in the third quadrant.
Therefore, cos(theta) = - 4/5 (because theta is in third quadrant).
=> (-3/5)^2 + cos^2(theta) = 1
=> 9/25 + cos^2(theta) = 1
=> cos^2(theta) = 1 - 9/25
=> cos^2(theta) = 16/25
=> cos(theta) = +/- 4/5
However, it is given that theta is between π and 3π/2, so this puts theta in the third quadrant.
Therefore, cos(theta) = - 4/5 (because theta is in third quadrant).
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