Question

cos x = - v3/2, x e 3º quadrante, dar as demais funções (sen, tg cotg, sec, cosec )

Answer 1

$cosx=- \frac{ \sqrt{3} }{2} \\ sen x^{2}+cos x^{2} =1 \\ sen x^{2} + \frac{3}{4}=1 \\ sen x^{2} =1- \frac{3}{4}= \sqrt{ \frac{1}{4} }= +/-\frac{1}{2}=- \frac{1}{2} \\ Tgx= \frac{senx}{cosx}= -\frac{1}{2}/- \frac{ \sqrt{3} }{2}= \frac{ \sqrt{3} }{3} \\cotgx= \frac{1}{ \frac{ \sqrt{3} }{3} }= \sqrt{3} \\ \\ secx= \frac{1}{ -\frac{ \sqrt{3} }{2} }= \frac{-2 \sqrt{3} }{3} \\ \\ cosecx= \frac{1}{ -\frac{1}{2} }=-2$