Question

вычислите tg a , если sin a = -√2/2 и π < a < 3 π/2

Answer 1

$tan( alpha) = frac{ sin( alpha ) }{ cos( alpha ) } = frac{ sin( alpha ) }{ sqrt{1 - { sin( alpha ) }^{2} } } \ frac{ frac{ - sqrt{2} }{2} }{ sqrt{1 - frac{1}{2} } } = - frac{ sqrt{2} }{2} div sqrt{ frac{1}{2} } = - frac{ sqrt{2} }{2} times sqrt{2} = - 1$