Evaluate: 1. tan 160°, cos 300° 2. sin 340°, cos 150° 3. sin 130°, sin(-70°), cos 350°

Right Triangle (opposite = 12, hypotenuse = 18)

Step 1: $\sin \theta = \frac{opposite}{hypotenuse}$.

Substitute: $\sin \theta = \frac{12}{18}$.

Simplify:
$\sin \theta = \frac{2}{3}$

Step 2: Adjacent side = $\sqrt{hypotenuse^2 - opposite^2}$.

Substitute: Adjacent side = $\sqrt{18^2 - 12^2} = \sqrt{324 - 144} = \sqrt{180}$.

Simplify:
$\sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}$

Step 3: $\cos \theta = \frac{adjacent}{hypotenuse}$.

Substitute: $\cos \theta = \frac{6\sqrt{5}}{18}$.

Simplify:
$\cos \theta = \frac{\sqrt{5}}{3}$

Step 4: $\tan \theta = \frac{opposite}{adjacent}$.

Substitute: $\tan \theta = \frac{12}{6\sqrt{5}}$.

Simplify:
$\tan \theta = \frac{2}{\sqrt{5}} = \frac{2\sqrt{5}}{5}$

Trigonometric Table (30°, 45°, 60°)

Using 30°-60°-90° triangle (sides opposite: $1$, $\sqrt{3}$, hypotenuse $2$).

Step 1: $\sin 30^\circ = \frac{opp (30°)}{hyp}$.

Substitute: $\sin 30^\circ = \frac{1}{2}$.

$\sin 30^\circ = \frac{1}{2}$

$\cos 30^\circ = \frac{adj (30°)}{hyp} = \frac{\sqrt{3}}{2}$.

$\cos 30^\circ = \frac{\sqrt{3}}{2}$

$\tan 30^\circ = \frac{opp (30°)}{adj (30°)} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$.

$\tan 30^\circ = \frac{\sqrt{3}}{3}$

Step 2: $\sin 60^\circ = \frac{opp (60°)}{hyp} = \frac{\sqrt{3}}{2}$.

$\sin 60^\circ = \frac{\sqrt{3}}{2}$

$\cos 60^\circ = \frac{adj (60°)}{hyp} = \frac{1}{2}$.

$\cos 60^\circ = \frac{1}{2}$

$\tan 60^\circ = \frac{opp (60°)}{adj (60°)} = \sqrt{3}$.

$\tan 60^\circ = \sqrt{3}$

Using 45°-45°-90° triangle (sides opposite: $1$, $1$, hypotenuse $\sqrt{2}$).

Step 3: $\sin 45^\circ = \frac{opp (45°)}{hyp} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$.

$\sin 45^\circ = \frac{\sqrt{2}}{2}$

$\cos 45^\circ = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$.

$\cos 45^\circ = \frac{\sqrt{2}}{2}$

$\tan 45^\circ = \frac{1}{1} = 1$.

$\tan 45^\circ = 1$

\sin \theta = 2/3, \cos \theta = \sqrt{5/3, \tan \theta = 2\sqrt{5}/5

30°: \sin=1/2, \cos=\sqrt{3}/2, \tan=\sqrt{3}/3

45°: \sin=\sqrt{2}/2, \cos=\sqrt{2}/2, \tan=1

60°: \sin=\sqrt{3}/2, \cos=1/2, \tan=\sqrt{3}}