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Algebra II Honors—Day 74

Algebra II Honors—Day 74. Reminders. No food/drinks/electronics. Put them all away NOW. Take-Home Test #8 Due Tuesday, May 6 Essential Question/New Material. Essential Questions. What is a radian, and how do I use it to determine angle measure on a circle?.

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Algebra II Honors—Day 74

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  1. Algebra II Honors—Day 74

  2. Reminders • No food/drinks/electronics. Put them all away NOW. • Take-Home Test #8 Due Tuesday, May 6 • Essential Question/New Material

  3. Essential Questions What is a radian, and how do I use it to determine angle measure on a circle?

  4. Review of Right Triangle Trigonometry Hypotenuse(longest side) Opposite (across from the angle) Adjacent (beside the angle) In Geometry, represented an acute angle in a right triangle. In this unit, we’ll extend this idea to let it include ALL angles. • From Geometry you learned:

  5. Angle Measures • Usually in Geometry, angles are measured in degrees. • A circle has 360⁰ • A half-circle has 180⁰ • A right angle measures 90⁰ • An alternate way to measure angles in a circle is in a measure called radians.

  6. Unit Circle/Angle Measures Arc length=1 unit (same as the radius of the circle) A unit circle is a circle centered at the origin with a radius of 1 unit. In a unit circle, a radian is defined as the measure of an angle whose rays intersect an arc length of 1 unit. In this diagram, the measure of the angle is one radian.

  7. Unit Circle/Angle Measures Since the circumference of a circle isand the circumference of the unit circle is , there are radians in a circle. Therefore, radians is equal to 360⁰.

  8. Unit Circle/Angle MeasuresMEMORIZE OR BE ABLE TO FIGURE OUT Angle measures begin from the positive x-axis. Positive angle measures turn counter-clockwise. To convert:degrees to radians multiply by radians to degrees multiply by http://teachers.henrico.k12.va.us/math/ito_08/Pics/UnitCircle.png

  9. Unit Circle/Angle MeasuresAdditional Notes Negative angle measures start from the positive x-axis but turn CLOCKWISE. Angle measures greater than 360⁰ (2π radians) or less than 0⁰ (0 radians) have “coterminal angles” that fall between 0⁰ and 360⁰ (or between 0 and 2π radians) in standard position.

  10. Unit Circle/Angle MeasuresAdditional Notes Example: an angle of 400⁰ would end up at the same location as a 40⁰ angle (so 400⁰ and 40⁰ are coterminal) (subtract a multiple of 360 for degrees or a multiple of 2π for radians) Example: an angle of –π/2 radians would end up at the same point as an angle of 3π/2 radians (add a multiple of 360 for degrees or a multiple of 2π for radians)

  11. http://www.regentsprep.org/regents/math/algtrig/ATT3/standardangle.gifhttp://www.regentsprep.org/regents/math/algtrig/ATT3/standardangle.gif http://aventalearning.com/content168staging/2008Trigonometry/unit3/images/MTH08-68.18243.jpg Angles between 0 and 2π are in “standard position.” http://images.tutorcircle.com/cms/images/tcimages/abc.gif

  12. Graded Classwork • With a partner or on your own, complete the Angles and Angle Measure handout. Turn in at the end of the period for a grade (one sheet for each pair of students)

  13. Homework • MEMORIZE THE UNIT CIRCLE and complete the problems on the sheet—Quiz next class period! • Work on Take-Home Test

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