Introduction to Trigonometry Angles and Radians (MA3A2): Define an understand angles measured in degrees and radians.

the rotating ray and the positive half of the x-axis angle

a positive angle whose vertex is at the center of a circle central angle

2 angles with a sum of 90 degrees complementary angles

2 angles in standard position that have the same terminal side coterminal angles

The beginning ray of an angular rotation; the positive half of the x- axis for an angle in standard position initial side

a clockwise measurement of an angle negative degree measure

Moving around a circle toward the right; a negative rotation Clockwise

a counterclockwise measurement of an angle positive degree measure

Opposite to clockwise; moving around the circle toward the left; a positive rotation counterclockwise

An angle in standard position with a terminal side that coincides with one of the four axes quadrantal angle

One of the 4 regions into which the x- and y-axes divide the coordinate plane quadrant

A unit of angle measure radian

The position of an angle with vertex at the origin, initial side on the positive x-axis, and terminal side in the plane standard position

2 angles with a sum of 180 degrees supplementary angles

The ending ray of an angular rotation; rotating ray terminal side

1 full revolution Obj: Find the quadrant in which the terminal side of an angle lies. half a revolution

¼ of a revolution Obj: Find the quadrant in which the terminal side of an angle lies. triple revolution

Quad. IQuad. II Quad. III Quad. IV 0 ◦ /360° 90 ◦ 180 ◦ 270 ◦

I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ In which quadrant does the terminal side of the angle lie? EX: 53°

I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ In which quadrant does the terminal side of each angle lie? EX: 253°

I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ EX: In which quadrant does the terminal side of each angle lie? EX: -126°

I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ EX: In which quadrant does the terminal side of each angle lie? EX: -373°

I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ EX: In which quadrant does the terminal side of each angle lie? EX: 460°

I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ ON YOUR OWN: In which quadrant does the terminal side of each angle lie? 1. 47° ° ° ° °

I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ ON YOUR OWN: In which quadrant does the terminal side of each angle lie? 1. 47° ° ° ° ° I III IV IIII

ON YOUR OWN: Draw each angle ° 6. 45° °9. 405°

ON YOUR OWN: Draw each angle ° 6. 45° °9. 405°

Θ (theta) Lowercase Greek letters are used to denote angles α (alpha) β (beta) γ (gamma)

EX: Θ = 60°. Finding Coterminal Angles (angles that have the same terminal side):

EX: Θ = 790°. Finding Coterminal Angles (angles that have the same terminal side): 1)Add and subtract from 360°, OR 2)Add and subtract from 2∏. EX: Θ = 440°. EX: Θ = -855°.

1. Θ = 790°. ON YOUR OWN: Find one positive and one negative coterminal angle.

Reference Angle: the acute angle formed by the terminal side and the closest x-axis. EX: Find the reference angle for each angle. Θ = 115°. **Reference angles are ALWAYS positive!! **Subtract from 180° or 360°.

Reference Angle: the acute angle formed by the terminal side and the closest x-axis. EX: Θ = 225°. **Reference angles are ALWAYS positive!! **Subtract from 180° or 360°.

Reference Angle: the acute angle formed by the terminal side and the closest x-axis. EX: Θ = 330° **Reference angles are ALWAYS positive!! **Subtract from 180° or 360°.

EX: Θ = -150°. Finding Reference Angles fpr Negative Angles: 1)Add 360° to find the coterminal angle. 2)Subtract from closest x-axis (180° or 360°).

EX: Θ = 60°. **If Θ lies in the first quadrant, then the angle is it’s own reference angle.

11. Θ = 210 ° 10. Θ = 405° 12. Θ = -300 °13. Θ = -225 ° ON YOUR OWN: Find the reference angle for the following angles of rotation.

11. Θ = 210 ° 10. Θ = 405° 12. Θ = -300 °13. Θ = -225 ° ON YOUR OWN: Find the reference angle for the following angles of rotation.

Converting Degrees to Radians *Multiply by ∏ radians 180 degrees EX: 60° EX: 225° EX: 300° EX: -315°

ON YOUR OWN: Convert to radian measure. Give answer in terms of ∏ ° ° ° ° °

ON YOUR OWN: Convert to radian measure. Give answer in terms of ∏ ° ° ° ° °

Converting Radians to Degrees *Multiply by 180 degrees ∏ radians EX:

ON YOUR OWN: Convert to Degrees ° -2160° 135° 225° 270°

ON YOUR OWN: Convert to Degrees

Finding Coterminal Angles *add or subtract from 360° *_____degrees ± 360 EX: 390° EX: 140° EX: -100°

Finding Complements and Supplements *To find the complement: subtract from 90° *To find the supplement: subtract from 180° EX: 35°EX: 120°