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

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

Simplify:

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

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

Simplify:

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

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

Simplify:

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

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).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$\tan 45^\circ = 1$$

\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}