Answer:
[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]
Step-by-step explanation:
we have that
The angle [tex]\theta[/tex] belong the the First Quadrant (see the figure)
so
[tex]cos(\theta)\ and\ sin(\theta)[/tex] are positive values
we know that
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex] ----> trigonometric identity
we have
[tex]sin(\theta)=\frac{2}{5}[/tex]
substitute in the identity
[tex](\frac{2}{5})^2+cos^2(\theta)=1[/tex]
[tex]cos^2(\theta)=1-\frac{4}{25}[/tex]
[tex]cos^2(\theta)=\frac{21}{25}[/tex]
square root both sides
[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]
