pencil, red pen, highlighter, calculator, notebook U8D3 Have out: pencil, red pen, highlighter, calculator, notebook Bellwork: Determine the value of x. 25° x 2 1) 2) 3) 20° x x 12 5 +1 +1 5 +1 +1 +1 +1 +1 exact +1 +1 +2 approx. total: +2 +2

The _______ side will fall into one of the four __________. terminal An angle θ is in _______ _______ on the xy–plane when its vertex is on the _______ and the ______ side is on the positive x–axis. standard position origin initial The _______ side will fall into one of the four __________. terminal quadrants y (0, 0) x y I x II IV III terminal side initial side

An angle is in: 90° 0° 90° y I x II IV III Quadrant I if ______ < < ______ 90° 180° Quadrant II if ______ < < ______ 180° 0° 180° 270° Quadrant III if ______ < < ______ Quadrant IV if ______ < < ______ 270° 360° 270° An angle whose terminal side falls on an axis is called a _________ angle. quadrantal The _________ angles are _____, _____, _____, _____, … quadrantal 0° 90° 180° 270°

Practice: In which quadrant or on which axis does the terminal side of each angle lie? Draw a sketch. 1) 140° 2) 210° 3) 300° 4) 450° y x y x y x y x Huh? Isn’t that 90o? II III IV positive y–axis Negative angles go in a ________ direction. 5) –200° 6) –120° 7) –180° clockwise y x y x y x II III negative x–axis

Radian Measure Given a circle with center O and radius r, draw a central angle such that the arc length is equal to the radius. (Hint: Use string and a protractor.) The measure of the angle is defined as __________. r one radian r O r How many degrees is one radian???

One radian is approximately ______ degrees. 57.3 One radian is approximately ______ degrees. Since the formula for the circumference of a circle is ________, there are ___ radians in one complete revolution of a circle. (let r = radians)

We know there are _____ in a circle, so _____ = _____ radians, or more simply, _____ = _____ radians. 360o 360o 180o 360o Now, solve for r.  We use this conversion when we go from _______ to _______. 1 radian = ≈ _____ 57.3o radians degrees  We use this conversion when we go from _______ to _______. 1° = radians degrees radians

Practice: Convert each to radian measure. 1) 90° 2) 270° 3) 60° 4) 120° 5) 200°

Practice: Convert each to degree measure. 1) 2) 3) 4) 5) NOTE: If you do not label the degree symbol, it is assumed that answer is in radians. Your answers will be marked incorrect!

 Record the radian measure on each of the _________ angles. quadrantal An angle is in: Quadrant I if ______ < < ______ y I x II IV III Quadrant II if ______ < < ______ Quadrant III if ______ < < ______ Quadrant IV if ______ < < ______

I II IV Practice: In which quadrant or on which axis does the terminal side of each angle lie? Convert to degrees. 1) 2) 3) y x y x y x I II IV

Practice: In which quadrant or on which axis does the terminal side of each angle lie? Convert to degrees. 4) 5) 6) y x y x y x negative y–axis IV III

Complete the rest of the worksheets.