Question

Given that sin0= 1/4,0 <0 < pi/2 , what is the exact value of cos 0 (picture provided)

Answer 1

Option b

Explanation:

By definition we know that:

`cos ^ 2(\theta) = 1- sin ^ 2(\theta)`

We know that for this case:

`sin(\theta) = (1)/(4)`

Then:

`cos ^ 2(\theta) = 1- ((1)/(4))^2\\\\cos ^ 2(\theta) = 1- ((1)/(16))\\\\cos ^ 2(\theta) = (15)/(16)\\\\`

Apply square root on both sides of the equation

`√(cos ^ 2(\theta)) = \sqrt{(15)/(16)}\\\\cos(\theta) = \sqrt{(15)/(16)}\\\\cos(\theta) = (√(15))/(4)`