Answer
We can see the completed table below:
Work Step by Step
$\theta = 90^{\circ}$ :
$x = 0$
$y = 1$
$r = 1$
We can find the trigonometric values:
$sin ~\theta = \frac{y}{r} = \frac{1}{1} = 1$
$cos ~\theta = \frac{x}{r} = \frac{0}{1} = 0$
$tan ~\theta = \frac{y}{x} = \frac{1}{0}$ (undefined)
$csc ~\theta = \frac{r}{y} = \frac{1}{1} = 1$
$sec ~\theta = \frac{r}{x} = \frac{1}{0}$ (undefined)
$cot ~\theta = \frac{x}{y} = \frac{0}{1} = 0$
$\theta = -360^{\circ} = 0^{\circ}$ :
$x = 1$
$y = 0$
$r = 1$
We can find the trigonometric values:
$sin ~\theta = \frac{y}{r} = \frac{0}{1} = 0$
$cos ~\theta = \frac{x}{r} = \frac{1}{1} = 1$
$tan ~\theta = \frac{y}{x} = \frac{0}{1} = 0$
$csc ~\theta = \frac{r}{y} = \frac{1}{0}$ (undefined)
$sec ~\theta = \frac{r}{x} = \frac{1}{1} = 1$
$cot ~\theta = \frac{x}{y} = \frac{1}{0}$ (undefined)
$\theta = 630^{\circ} = 270^{\circ}$ :
$x = 0$
$y = -1$
$r = 1$
We can find the trigonometric values:
$sin ~\theta = \frac{y}{r} = \frac{-1}{1} = -1$
$cos ~\theta = \frac{x}{r} = \frac{0}{1} = 0$
$tan ~\theta = \frac{y}{x} = \frac{-1}{0}$ (undefined)
$csc ~\theta = \frac{r}{y} = \frac{1}{-1} = -1$
$sec ~\theta = \frac{r}{x} = \frac{1}{0}$ (undefined)
$cot ~\theta = \frac{x}{y} = \frac{0}{-1} = 0$
We can see the completed table below:
