Solving Right Triangles and the Unit Circle 30 November 2010

Inverse Trigonometric Functions We can “undo” trig functions by using the correct inverse trig function Gives us the angle measurement (theda) Represented with a small –1 in the upper right hand corner Ex. 2nd button → correct trig function

Inverse Trigonometric Functions, cont.

Your Turn: Solve for theda

Solving Right Triangles If given two sides of a triangle, then we can solve for any of the angles of the triangle. 4 5

Solving Right Triangles, cont. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse? Pick the appropriate trig function to solve for Solve for using the inverse trigonometric function 4 5

Solving Right Triangles, cont. 4 5

Your Turn: Pg. 430: 25 – 28

The Unit Circle – Introduction Circle with radius of 1 1 Revolution = 360° 2 Revolutions = 720° Positive angles move counterclockwise around the circle Negative angles move clockwise around the circle

Coterminal Angles co – terminal Coterminal Angles – Angles that end at the same spot with or joint ending

Coterminal Angles, cont. Each positive angle has a negative coterminal angle Each negative angle has a positive coterminal angle Coterminal angles are equivalent Example: 90° = –270°

Coterminal Examples 30° 390° 750° –330°

On a separate sheet of paper, find three coterminal angles with the given angle measure. One of the angles must be negative. 1. 45° 2. 250° 3. –20° 4. 720° 5. –200°

Radian Measure Another way of measuring angles Convenient because major measurements of a circle (circumference, area, etc.) are involve pi Radians result in easier numbers to use