Question

Calcule: Cos (Arc Sen 1/4).​

Answer 1

Explicação passo-a-passo:

relaçao fundamental trigonometrica

cos²(Arcsen 1/4) + sen² (arcsen1/4) = 1

cos²(arcsen1/4)+ 1/16 = 1

cos²(arcsen1/4) = 1-1/16

cos²(arcsen1/4) = 15 /16

cos(arcsen1/4) = √15/4

Answer 2

$\Large\boxed{\begin{array}{l}\sf cos\bigg(arc~sen\bigg(\dfrac{1}{4}\bigg)\bigg)\\\sf arc~sen\bigg(\dfrac{1}{4}\bigg)=\alpha\\\\\sf sen(\alpha)=\dfrac{1}{4}\\\\\sf cos^2(\alpha)=1-sen^2(\alpha)\\\sf cos^2(\alpha)=1-\bigg(\dfrac{1}{4}\bigg)^2\\\\\sf cos^2(\alpha)=1-\dfrac{1}{16}=\dfrac{15}{16}\\\\\sf cos(\alpha)=\dfrac{\sqrt{15}}{\sqrt{16}}\\\\\sf cos(\alpha)=\dfrac{\sqrt{15}}{4} \end{array}}$