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valina [46]
3 years ago
14

What is the exact value? (Picture provided)

Mathematics
2 answers:
creativ13 [48]3 years ago
6 0

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

kow [346]3 years ago
6 0

Answer:

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

Step-by-step explanation:

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

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}

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