美国高中数学3-11 Polar and Complex 极坐标与复数.doc

    11-1: Polar Coordinates and Complex Numbers   Important things to remember!!  Converting from polar to rectangular: 1) x = r cos 0 2) y = r sin 0 Converting from rectangular to polar:  3) r2 = x2 + y2 4) tan 0 = (y/x) Click for polar graphing calculator! (Manipula Math)   Example problems 1) Change (3, 4) to polar coordinates. Solution: Using property 3 from above, find r.   32 + 42 = 25 and take the square root.                 Therefore, r = 5 Using property 4 from above, tan 0 = (4/3). Use your calculator set to degree mode, the answer is: 53.1 degrees. (rounded to nearest tenth.                 Therefore, the point is ( 5, 53.1o) 2) Change ( 4, 150o) to rectangular coordinates Solution: Using property 1 from above x = 4 cos 150. Using your calculator you get x = -3.46 rounded to hundredths. Using property 2 from above y = 4 sin 150. Using your calculator you get y = 2              Therefore, the point is ( -3.46, 2)  3) Change (-3, -7) to polar coordinates Solution: Using property 3 from above find r. Square -3 and add to the square of -7 you get 58 and taking the square root on your calculator means r = 7.6   Piece of cake! To find theta we use property 4, tan 0 = 7/3. Notice I used positive values! I did this to find the reference angle in quad I. The reference angle is equal to 66.8 degrees. Since we are in quadrant III, (look at the signs of the original problem) we should add 180. Why? ( we are in quad III and we memorized we add 180 in that quad, right?) So the angle is 246.8o.             Therefore, the point is (7.6, 246.8o) ( all to simple!!!)    Note You can use the special functions on the TI-82 to find all the above answers.  Make sure your calculator is set in degree mode(if you want the answer in degrees) and press 2nd function angle.  This takes you to a menu that has choice 5 and 6 to change to polar form.  Choice 5 gives you the radius and choice 6 gives you the theta value.  Example (1,3) Get to choice 5 on your calculator: Y