Answer
$\sin\theta=\frac{y}{r}=\frac{\sqrt 5}{7}$
$\cos\theta=\frac{x}{r}=\frac{\sqrt {44}}{7}$
$\tan\theta=\frac{y}{x}=\frac{\sqrt 5}{\sqrt{44}}=\frac{\sqrt {220}}{44}$
$\cot\theta=\frac{x}{y}=\frac{\sqrt {44}}{\sqrt 5}=\frac{\sqrt {220}}{ 5}$
$\sec\theta=\frac{r}{x}=\frac{7}{\sqrt {44}}\frac{7\sqrt {44}}{44}$
$\csc\theta=\frac{r}{y}=\frac{7}{\sqrt 5}=\frac{7\sqrt 5}{5}$
Work Step by Step
1.Angle in quadrant I, x is positive and y is negative
Given values $y=\sqrt 5$ and $r=7$
2. Using given values and distance formula, we can find the x
$7=\sqrt {(x)^{2}+(\sqrt 5)^{2}}$
$49=5+x^{2}$
$x=\sqrt {44}$
3.Plug the values to find trig functions
$\sin\theta=\frac{y}{r}=\frac{\sqrt 5}{7}$
$\cos\theta=\frac{x}{r}=\frac{\sqrt {44}}{7}$
$\tan\theta=\frac{y}{x}=\frac{\sqrt 5}{\sqrt{44}}=\frac{\sqrt {220}}{44}$
$\cot\theta=\frac{x}{y}=\frac{\sqrt {44}}{\sqrt 5}=\frac{\sqrt {220}}{ 5}$
$\sec\theta=\frac{r}{x}=\frac{7}{\sqrt {44}}\frac{7\sqrt {44}}{44}$
$\csc\theta=\frac{r}{y}=\frac{7}{\sqrt 5}=\frac{7\sqrt 5}{5}$
