LESSON 6-1: ANGLES & THE UNIT CIRCLE BASIC GRAPHING OBJECTIVE: CONVERT BETWEEN DEGREE AND RADIAN MEASURE, PLACE ANGLES IN STANDARD POSITION & IDENTIFY CO-TERMINAL ANGLES, UNDERSTAND BASIC GRAPHS OF COSINE AND SINE.

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side Any angle drawn from the origin with an initial side and terminal side

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side Any angle drawn from the origin with an initial side and terminal side Any two angle with the same terminal side, whether it open counter-clockwise or clockwise

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side Any angle drawn from the origin with an initial side and terminal side Any two angle with the same terminal side, whether it open counter-clockwise or clockwise The angle between the terminal side and the x-axis

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y A circle drawn about the origin with radius = 1

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y A circle drawn about the origin with radius = 1 The opening equivalent to one radius wrapped around circumference of the unit circle

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y A circle drawn about the origin with radius = 1 The opening equivalent to one radius wrapped around circumference of the unit circle

VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y 1 st draw where you think the angle ends

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y Find the quadrants by remembering their placement

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y x y Find the reference angle by remembering That it is always formed with x-axis

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y Try this one

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y Now this one Let’s check our work

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y x y

Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y x y

Checkpoint

COTERMINAL ANGLES

HOW DO I FIND COTERMINAL ANGLES? EXAMPLE: FIND ONE POSITIVE AND ONE NEGATIVE COTERMINAL ANGLE OF 315 O

RADIANS ↔ DEGREES CONVERTING BETWEEN DEGREES AND RADIANS: SET UP THE RATIO AND SOLVE FOR THE MISSING

RADIANS ↔ DEGREES Try converting these measures

RADIANS ↔ DEGREES

Here are some more to try

RADIANS ↔ DEGREES

Checkpoint