Question

Seja cos ⁡α = -1/3, com π < α < 3π/2, qual o valor da tg α?

Answer 1

Resposta:

$tg\alpha =2\sqrt{2}$

Explicação passo-a-passo:

$Sendo~cos\alpha =-\frac{1}{3\impliessec } \implies sec\alpha =-3\\\\\alpha~~no~~3\°~~quadrante,~~tg\alpha >~0\\\\1+tg^2\alpha =sec^2\alpha \\\\tg^2\alpha =(-3)^2-1\\\\tg^2\alpha =9-1\\\\tg^2\alpha =8\\\\tg\alpha =\sqrt{4.2} \\\\tg\alpha =2\sqrt{2}$