Question

Se x=arcsen15/17, então o valor de cosx é:
a) 5/17  b)7/15  c)8/17  d)4/15  e)8/15

Answer 1

$sen(x)=\frac{15}{17}\\ \\ cos(x)= \sqrt{1-(\frac{15}{17})^2} \\ \\ cos(x)= \sqrt{1-\frac{225}{289}}\\ \\ cos(x)= \sqrt{\frac{64}{289}}=\frac{8}{17}$

Answer 2

arcsen = sen(x)

sen²x + cos²x = 1²

(15/17)² + cos²x = 1²

cos²x = 1² - (15/17)²

cos²x = 1 - 225/289

cos²x = 64/289

cos(x) = $\sqrt{64/289}$

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cos(x) = 8/17
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