Question

What is the exact value? (Picture provided)

Answer 1

Answer:

b.  (√15)/4

Step-by-step 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

Answer:

b. $\frac{\sqrt{15}}{4}$

Step-by-step explanation:

Given that $\sin(\theta)=\frac{1}{4}$ where $0\:<\: \theta \:<\:\frac{\pi}{2}$.

Recall and use the Pythagorean Identity;

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

This implies that;

$(\frac{1}{4})^2+\cos^2(\theta)=1$

$\frac{1}{16}+\cos^2(\theta)=1$

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

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

Take the square root of both sides;

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

$\cos(\theta)=\pm \frac{\sqrt{15}}{4}$

Since we are in the first quadrant;

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