1. Trigonometry What is trigonometry? Trigonometry (from the Greek trigonon = three angles and metro = measure [1]) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent.Greek[1]mathematicsanglestrianglestrigonometric functionssinecosinetangent

2. 1. Draw a right triangle with appropriate labels. Identify the following: Hypotenuse, Opposite side, Adjacent side 2. Define the 6 trig functions using the three terms in #1. Write the Pythagorean formula. 3. What are complimentary angles? 4. What are supplementary angles? 5. What is an acute angle? 6. What is an obtuse angle? 7. What is a straight angle? 9. How many degrees in a triangle? 10. How many degrees in a circle? Trigonometry Pre-Assessment

3.  Angles: acute, right, obtuse  Greek notation: , , , , ,   Review right triangles  SOH-CAH-TOA  Complimentary angles  Supplementary angles Trigonometry

4. Purpose: to compare the measures of angle with a vertex at the origin on a coordinate plane.  The measure of an angle in standard position is the input for two important functions. The outputs are the coordinates (called sine and cosine) of the point on the terminal side of the angle that is 1 unit from the origin.  Two angles in standard position are coterminal if they have the same terminal side. Angles and Unit Circle

5.  Quadrants: Quadrantal angles  Measuring angles in standard position  Angle in Standard Position: an angle is in standard position if its initial side is on the positive x-axis and the vertex is @ the origin.  Clockwise rotation  Counterclockwise rotation Angles and Unit Circle

6.  Smartboard presentation on angles in standard position.  Radians Angles and Unit Circle

7.  A central angle of a circle is an angle with a vertex at the origin of the circle.  An intercepted arc is the portion of the circle with endpoints on the sides of the central angle and remaining points within the interior of the angle.  A radian is the measure of a central angle that intercepts an arc with length equal to the radius of the circle. Radian = arc length/radius  Radians, like degrees, measure the amount of rotation from the initial side to the terminal side of an angle. 1 radian = 57.296º Angles and Unit Circle

8.  Establish relationship between degrees/radians Angles and Unit Circle DegreesRadians 360º2π 180ºπ 90ºπ/2 45ºπ/4 30ºπ/6

9.  Convert from degrees to radians or radians to degree ratio: d  /180  = r radians/  radians or d  = 180  r radians/  radians R radians =   d  /180  Angles and Unit Circle

10. Examples: convert 60  to radians convert  /6 to degrees Angles and Unit Circle

12. Assignment: Draw the following in standard position. 1.60  5. 120  2.225  6. 300  3.- 30  7. - 90  4.- 145  8. Find the measure of an angle between 0  and 360 , which are co-terminal with each given angle. a. - 60  b. 200  c. - 270  Angles and Unit Circle