Question

Dada secx = 4, calcule o valor da cossecx, sendo x um ângulo pertencente ao 1° quadrante.

Answer 1

$\large\boxed{\begin{array}{l}\rm tg^2(x)=sec^2(x)-1\\\rm tg^2(x)=4^2-1\\\rm tg^2(x)=16-1\\\rm tg^2(x)=15\\\rm tg(x)=\sqrt{15}\longrightarrow cotg(x)=\dfrac{1}{\sqrt{15}}\\\\\rm cossec^2(x)=1+cotg^2(x)\\\rm cossec^2(x)=1+\bigg(\dfrac{1}{\sqrt{15}}\bigg)^2\\\\\rm cossec^2(x)=1+\dfrac{1}{15}\\\\\rm cossec^2(x)=\dfrac{16}{15}\\\\\rm cossec(x)=\dfrac{\sqrt{16}}{\sqrt{15}}\\\\\rm cossec(x)=\dfrac{4}{\sqrt{15}}=\dfrac{4\sqrt{15}}{15}\end{array}}$

Answer 2

cosseResposta:

4√15/15

Explicação passo a passo:

secx = 4 ⇒ cosx = 1/4

sen²x + cos²x = 1

sen²x  +(1/4)² = 1

sen²x  + 1/16 = 1

sen²x = 1 - 1/16

sen²x = (16 -1 )/16

sen²x = 15/16

senx = √15/4 ( pois x é do 1° quadrante)

cossecx = 4/√15 = 4√15/15