Given that sin theta= 1/4, 0 is less than theta but less than pi/2, what is the exact value of cos theta

Question

asked Nov 22, 2021 42.2k views

2 Answers

Gurneet Sethi · Answer 1 · 2021-11-27T08:02:07+0000

Answer:

$cos(\theta) = (√(15))/(4)$

Explanation:

For any angle
$\theta$ , we have that:

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

Quadrant:

$0 \leq \theta \leq (\pi)/(2)$ means that
$\theta$ is in the first quadrant. This means that both the sine and the cosine have positive values.

Find the cosine:

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

$((1)/(4))^(2) + (cos(\theta))^(2) = 1$

$(1)/(16) + (cos(\theta))^(2) = 1$

$(cos(\theta))^(2) = 1 - (1)/(16)$

$(cos(\theta))^(2) = (16-1)/(16)$

$(cos(\theta))^(2) = (15)/(16)$

$cos(\theta) = \pm \sqrt{(15)/(16)}$

Since the angle is in the first quadrant, the cosine is positive.

$cos(\theta) = (√(15))/(4)$