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Aleesha guide to evaluating and converting


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Aleesha guide to evaluating and converting

  1. 1. Guide to Evaluating and converting<br />A math methods presentation by Aleesha Davis<br />
  2. 2. Convert<br />Definition - a change in the form of a quantity, a unit, or an expression without a change in the value <br />The angle, in radians, swept out in one revolution of a circle is 2πc ( c is equal to radians)<br />2πc = 360°<br />Therefore, πc = 180°<br />1c = 180°<br />π<br /> 1° = πc <br /> 180<br />
  3. 3. Convert<br />When converting from degrees to radians, <br />When converting from radians to degrees,<br />
  4. 4. convert<br />Example <br />Convert 30° to radians<br />Solution<br />Since 1° = πc <br /> 180<br /> 30° = 30 × πc <br /> 180<br /> = πc <br /> 6<br />
  5. 5. Convert<br />Questions to complete<br />Exercise 6A, Questions 1-4<br />Tips<br />Make sure your calculator is in the correct mode; radians or degrees depending on what question you are doing<br />
  6. 6. Evaluate<br />Definition -  To calculate the numerical value of; express numerically<br /> The unit circle is a circle of radius 1 unit.<br />P(θ) = (cos θ, sin θ)<br />
  7. 7. Evaluate<br />Using symmetry properties of the unit circle, we can determine how properties in each quadrant are written, and which of the trigonometric functions are positive. As displayed, in quadrant 1-all sin, cosine and tan are positive, in quadrant 2-only sin is positive, in quadrant 3-only tan is positive, and in quadrant 4-only cosine is positive.<br />
  8. 8. Evaluate<br />Example 1<br />Evaluate sin π and cos π<br />Solution<br />In moving through an angle of π, the position P(π), which is (-1,0).<br />Therefore, cos π = -1<br />and sin π = 0<br />
  9. 9. Evaluate<br />For the unit circle, the trigonometry ratios for the reference angles in the first quadrant are shown below. We use 30o-60o-90o and 45o-45o-90o triangles to determine these ratios.<br />
  10. 10. Evaluate<br />Example<br />Evaluate cos <br />Solution<br />cos = cos(π + )<br /> =–cos (by symmetry)<br /> =<br />Note– Symmetry properties can be found on page 199<br />
  11. 11. Evaluate<br />Questions to complete<br />Exercise 6B – Questions 2 all, 3 all, 4*<br />Exercise 6C – Questions 1* and 3*<br />Exercise 6E – Questions 1 and 2<br />