Question

Dado que tga = -2e < a < π, determinar o valor de sena e de cosa.
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Answer 1

$\large\boxed{\begin{array}{l}\sf tg(a)=-2\implies tg^2(a)=4\\\sf sec^2(a)=1+tg^2(a)\\\sf sec^2(a)=1+4\\\sf sec^2(a)=5\\\sf sec(a)=-\sqrt{5}\\\sf cos(a)=-\dfrac{1}{\sqrt{5}}=-\dfrac{\sqrt{5}}{5}\\\sf sen(a)= cos(a)\cdot tg(a)\\\sf sen(a)=-\dfrac{\sqrt{5}}{5}\cdot-2\\\sf sen(a)=\dfrac{2\sqrt{5}}{5}\end{array}}$