Question

Se Tang(x)= 3/5, calcule o valor da sec(x)
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Answer 1

Lembrete:

๏ $\mathsf{sec\left(x\right)=\dfrac{1}{cos\left(x\right)}}$
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Dados:

๏ $\mathsf{tg\left(x\right)=\dfrac{3}{5}}$
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Logo:

$\mathsf{tg\left(x\right)=\dfrac{3}{5}}\\\\\mathsf{\dfrac{sen\left(x\right)}{cos\left(x\right)}=\dfrac{3}{5}}\\\\\mathsf{sen\left(x\right)\cdot \dfrac{1}{cos\left(x\right)}=\dfrac{3}{5}}\\\\\mathsf{sen\left(x\right)\cdot sec\left(x\right)=\dfrac{3}{5}}\\\\\mathsf{sec\left(x\right)=\dfrac{3}{5}\cdot \dfrac{1}{sen\left(x\right)}}\\\\\boxed{\mathsf{sec\left(x\right)=\frac{3\cdot cossec\left(x\right)}{5}}}$