Question

What is the exact value? (Picture provided)

Answer 1

b. (√15)/4

Explanation:

Since Sin Ф = (opposite side)/Hypotenuse, we have 2 sides of a right triangle.

Use Pythagorean theorem to solve for the missing leg (the adjacent side)

1² + b² = 4²

1 + b² = 16

b² = 15

b = √15

So the adjacent side is √15, so Cos Ф = (√15)/4

Answer 2

b.
`(√(15))/(4)`

Explanation:

Given that
`\sin(\theta)=(1)/(4)` where
`0\:<\: \theta \:<\:(\pi)/(2)`.

Recall and use the Pythagorean Identity;

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

This implies that;

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

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

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

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

Take the square root of both sides;

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

`\cos(\theta)=\pm (√(15))/(4)`

Since we are in the first quadrant;

`\cos(\theta)=(√(15))/(4)`