Question

The Pythagorean Identity states that:(sin x)2 + (cos x)2 = 1Given cos 0 = 4y2, find sin 0. .sin 8 =[?]Simplify the fraction.

Answer 1

`\sin (\theta)=\frac{\sqrt[]{17}}{49}`

1) Considering the Pythagorean Identity let's plug into that the value of cos (theta):

`\begin{gathered} \sin ^2(\theta)+\cos ^2(\theta)=1 \\ \sin ^2(\theta)=1-\cos ^2(\theta) \\ \sin ^2(\theta)=1-(\frac{4\sqrt[]{2}}{7})^2 \\ \sin ^2(\theta)=1-((32)/(49)) \\ \sin ^2(\theta)\text{ =}(17)/(49) \\ \sin (\theta)=\frac{\sqrt[]{17}}{49} \end{gathered}`

2) Since there's no way to reduce that fraction, we can state that sin(theta) is square root of 1