Question

IF 180°<theta< 270° and sintheta=-4/5
calculate sin(theta/2)
and cos(theta/2)
​

Answer 1

Answer:

$sin \alpha = - \frac{4}{5} \: so \: cos \alpha = - \frac{3}{5}$

$180 < \alpha < 270 \: then \: \: \: 90 < \frac{ \alpha }{2} < 135$

now, we know that

$2 \cos {}^{2} ( \frac{ \alpha }{2} ) - 1 = cos \: \alpha = - \frac{3}{5}$

$\cos {}^{2} ( \frac{ \alpha }{2} ) = (1 - \frac{3}{5} ) \div 2 = \frac{1}{5}$

$\cos( \frac{ \alpha }{2} ) = - \frac{1}{ \sqrt{5} }$

because in 2nd quadrant, Cos is negative

Answer 2

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