Question

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

Answer 1

Answer:

Option b

Step-by-step explanation:

By definition we know that:

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

We know that for this case:

$sin(\theta) = \frac{1}{4}$

Then:

$cos ^ 2(\theta) = 1- (\frac{1}{4})^2\\\\cos ^ 2(\theta) = 1- (\frac{1}{16})\\\\cos ^ 2(\theta) = \frac{15}{16}$

Apply square root on both sides of the equation

$\sqrt{cos ^ 2(\theta)} = \sqrt{\frac{15}{16}}\\\\cos(\theta) = \sqrt{\frac{15}{16}}\\\\cos(\theta) = \frac{\sqrt{15}}{4}$