cosine (θ) = 4/5
1) Given that the sin(θ) is in Quadrant I , and θ lies in this quadrant too
Let's remind the signal fo that:
2) Let's use the Pythagorean Identity to find the value of the cosine (θ):
[tex]\begin{gathered} \sin ^2(\theta)\text{ +}\cos ^2(\theta)\text{ =1} \\ (\frac{3}{5})^2+\cos ^2(\theta)\text{ =1} \\ \cos (\theta)\text{ =}\sqrt[]{1-\frac{9}{25}} \\ \cos \text{ (}\theta)\text{ =}\sqrt[]{\frac{25}{25}-\frac{9}{25}} \\ \cos \text{ (}\theta)\text{ =}\sqrt[]{\frac{16}{25}} \\ \cos \text{ (}\theta)=\frac{4}{5} \end{gathered}[/tex]
3) As the value of the sine and the cosine in Quadrant I is positive then we can state the cosine (θ) = 4/5
