Question

Se cos a = - 1/4 e π/2 ≤x ≤ π , calcule :

a)Sen a b) tg a c)sec a d) cossec a e) cotg a

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Answer 1

$\boxed{\begin{array}{l}\sf cos(a)=-\dfrac{1}{4}\implies cos^2(a)=\dfrac{1}{16}\\\rm a) ~\sf sen^2(a)=\dfrac{16}{16}-\dfrac{1}{16}=\dfrac{15}{16}\\\sf sen(a)=\dfrac{\sqrt{15}}{\sqrt{16}}=\dfrac{\sqrt{15}}{4}\\\rm b)~\sf tg(a)=\dfrac{\frac{\sqrt{15}}{\diagdown\!\!\!4}}{-\frac{1}{\diagdown\!\!\!4}}=-\sqrt{15}\\\rm c)~\sf sec(a)=-4\\\rm d)~\sf cossec(a)=\dfrac{4}{\sqrt{15}}=\dfrac{4\sqrt{15}}{15}\\\rm e)~\sf cotg(a)=-\dfrac{\sqrt{15}}{15}\end{array}}$