1. Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?

2. Trigonometry vocabulary Initial side – start side of angle Terminal side – end side of angle Standard position – An angle whose initial side is on the positive x-axis Coterminal angle – Angles that have the same terminal side Reference angle – The acute angle formed by the terminal side of the given angle and the x-axis. Standard Position - An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.

3. Positive angles Initial side on the positive x-axis and rotate counterclockwise

4. Negative angles Initial side on the positive x-axis and rotate clockwise

5. Quadrants Quadrant III Quadrant I Quadrant II Quadrant IV

6. Angles of the axes

7. Standard Position An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

8. Examples What quadrant is the terminal side of the angle in? (Make a sketch of the angle)

9. Reference angles The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Reference angles may appear in all four quadrants. Angles in quadrant I are their own reference angles.

10. Examples What are the reference angles for each of these angles?

11. Radians Angle degrees can also be expressed in radians Radians is the ratio of the length of an arc to its radius Radians are expressed in terms of = 180 o To change from degrees to radians, multiply by and reduce. To change from radians to degrees, multiply by

12. Examples Change from degrees to radians Change from radians to degrees

13. Examples - Coterminal angles You can add or subtract multiples of 360 or -360 to find coterminal angles Find 2 coterminal angles (one positive and one negative) for 35 o Find 2 coterminal angles (one positive and one negative) for -23 o Find 2 coterminal angles (one positive and one negative) for 740 o

14. Coterminal Examples using radians Add or subtract 2π to angle