Trigonometry – Special Angles

Angles in Standard Position

1. Sketch \theta=30^\circ in standard position.
2. Locate Quadrants I to IV.
3. \theta=700^\circ
   1. Sketch in standard position.
   2. Reference angle?
4. Given \pi radians equals 180^\circ
   1. Sketch \theta=\frac{\pi}{6} in standard position.
   2. Sketch \theta=\frac{\pi}{4} in standard position.
   3. Evaluate \sin 30^\circ on your calculator in Degree mode
   4. Evaluate \sin \frac{\pi}{6} in Radian mode

Special Angles

Solve the 1-2-\sqrt{3} triangle.

Solve the 1-1-\sqrt{2} triangle.

Evaluate without a calculator:

1. \sin 30^\circ\sin 45^\circ\sin 60^\circ\cos 30^\circ\cos 45^\circ\cos 60^\circ\tan 30^\circ\tan 45^\circ\tan 60^\circ

Evaluate the following special angles:

1. \sin 120^\circ\cos 135^\circ\tan (-690^\circ)-\sin 225^\circ

Evaluate the following quadrantal angles:

1. \sin 180^\circ\cos(-180^\circ)\sin 270^\circ\tan(360^\circ)

If \sin \theta is negative and \cos \theta is positive, what quadrant must \theta be in?