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