Answer
1. $\theta$ = 30$^{\circ}$
$\sin$ $\theta$ = $\frac{1}{2}$ , $\cos$ $\theta$ = $\frac{\sqrt 3}{2}$ , $\tan$ $\theta$ = $\frac{1}{\sqrt 3}$
$\csc$ $\theta$ = 2 , $\sec$ $\theta$ = $\frac{2}{\sqrt 3}$ , $\cot$ $\theta$ = ${\sqrt 3}$
2. $\theta$ = 45$^{\circ}$
$\sin$ $\theta$ = $\frac{1}{\sqrt 2}$ , $\cos$ $\theta$ = $\frac{1}{\sqrt 2}$ , $\tan$ $\theta$ = 1
$\csc$ $\theta$ = $\sqrt 2$ , $\sec$ $\theta$ = $\sqrt 2$ , $\cot$ $\theta$ = 1
3. $\theta$ = 60$^{\circ}$
$\sin$ $\theta$ = $\frac{\sqrt3}{2}$ , $\cos$ $\theta$ = $\frac{1}{2}$ , $\tan$ $\theta$ = $\sqrt3$
$\csc$ $\theta$ = $\frac{2}{\sqrt3}$ , $\sec$ $\theta$ = 2 , $\cot$ $\theta$ = $\frac{1}{\sqrt3}$
Work Step by Step
The best way to complete this question is to draw a unit triangle and verify through functions on your calculator. Make sure it is set to degrees, and complete the table.
1. $\theta$ = 30$^{\circ}$
$\sin$ $\theta$ = $\sin$ 30$^{\circ}$ = $\frac{1}{2}$
$\cos$ $\theta$ = $\cos$ 30$^{\circ}$ = $\frac{\sqrt 3}{2}$
$\tan$ $\theta$ = $\tan$ 30$^{\circ}$ = $\frac{1}{\sqrt 3}$
$\csc$ $\theta$ = $\csc$ 30$^{\circ}$ = 2
$\sec$ $\theta$ = $\sec$ 30$^{\circ}$ = $\frac{2}{\sqrt 3}$
$\cot$ $\theta$ = $\cot$ 30$^{\circ}$ = ${\sqrt 3}$
2. $\theta$ = 45$^{\circ}$
$\sin$ $\theta$ = $\sin$ 45$^{\circ}$ = $\frac{1}{\sqrt 2}$
$\cos$ $\theta$ = $\cos$ 45$^{\circ}$ = $\frac{1}{\sqrt 2}$
$\tan$ $\theta$ = $\tan$ 45$^{\circ}$ = 1
$\csc$ $\theta$ = $\csc$ 45$^{\circ}$ = $\sqrt 2$
$\sec$ $\theta$ = $\sec$ 45$^{\circ}$ = $\sqrt 2$
$\cot$ $\theta$ = $\cot$ 45$^{\circ}$ = 1
3. $\theta$ = 60$^{\circ}$
$\sin$ $\theta$ = $\sin$ 60$^{\circ}$ = $\frac{\sqrt3}{2}$
$\cos$ $\theta$ = $\cos$ 60$^{\circ}$ = $\frac{1}{2}$
$\tan$ $\theta$ = $\tan$ 60$^{\circ}$ = $\sqrt3$
$\csc$ $\theta$ = $\csc$ 60$^{\circ}$ = $\frac{2}{\sqrt3}$
$\sec$ $\theta$ = $\sec$ 60$^{\circ}$ = 2
$\cot$ $\theta$ = $\cot$ 60$^{\circ}$ = $\frac{1}{\sqrt3}$
From examining this table further, you may notice trends among the different Trig. Functions.
