TRIGONOMETRY AND THE UNIT CIRCLE SEC LEQ: How can you use a unit circle to find trigonometric values?

Sine, Cosine, and Tangent  Sine, cosine, and tangent can be defined for all real numbers  In a right triangle, the two angles other than the right angle measure between 0° and 90°  To define sines and cosines for all numbers, we use rotations with center (0, 0)  Positive angles are measured counter-clockwise  Negative angles are measured clockwise

Unit Circle  The circle with center at the origin and radius 1 unit  If the point (1, 0) on the circle is rotated around the origin with a magnitude θ, then the image point (x, y) is also on the circle  The coordinates of the image point can be found using sines and cosines  Which coordinate corresponds to sine?  y coordinate  The leg opposite the angle will be vertical  Which coordinate corresponds to cosine?  x coordinate  The leg adjacent the angle will be horizontal  (cos θ, sin θ )

For example  What are the coordinates of the image of (1, 0) under R 60 ?  R 60 (1, 0) = (cos 60, sin 60)

Rotations of More than 360°  More than one complete revolution  Example: Find cos 630° Remove the complete revolution 630 – 360 = 270 cos 630° = cos 270° cos 270° = 0  Find sin (-675°) Remove the complete revolutions = 45 sin (-675°) = sin 45°

Your Turn  Lesson Master 10-4A #1, 3, 5, 6, 9, 11, 14-21

Homework  Pgs #1-30