Answer:
[tex]\frac{\sqrt{55}}{8}[/tex]
Step-by-step explanation:
[tex]\sin(\theta)=\frac{3}{8}[/tex] is given.
We are also given that [tex]\theta[/tex]'s angle terminates in quadrant one which means all 6 trig ratios are positive there.
We will use Pythagorean Identity: [tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex].
[tex](\frac{3}{8})^2+\cos^2(\theta)=1[/tex]
[tex]\frac{9}{64}+\cos^2(\theta)=1[/tex]
[tex]\cos^2(\theta)=1-\frac{9}{64}[/tex]
[tex]\cos^2(\theta)=\frac{64-9}{64}[/tex]
[tex]\cos^2(\theta)=\frac{55}{64}[/tex]
[tex]\cos(\theta)=\pm \sqrt{\frac{55}{64}}[/tex]
[tex]\cos(\theta)=\frac{\sqrt{55}}{8}[/tex].
