Question

Sendo β a medida de um arco do 1º quadrante e sec β = 4/3, determine o valor de cossec β *

Answer 1

$\blue{\boxed{\begin{array}{l}\sf sec(\beta)=\dfrac{4}{3}\\\sf cos(\beta) =\dfrac{3}{4}\implies cos^2(\beta) =\dfrac{9}{16}\\\sf sen^2(\beta)=\dfrac{16}{16}-\dfrac{9}{16}\\\sf sen^2(\beta)=\dfrac{7}{16}\\\sf sen(\beta)=\dfrac{\sqrt{7}}{4}\\\sf cossec(\beta)=\dfrac{4}{\sqrt{7}} \\\sf cossec(\beta)=\dfrac{4\sqrt{7}}{7}\end{array}}}$