Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
01 trigonometric ratios of any angle in standard position.notebook page 466 - 6.1 Trigonometric Ratios for Any Angle in Standard Position November 12, 2012 Special Triangles and Exact Values for the Trigonometric Ratios 30o - 60o - 90o Triangles Special Triangles and Exact Values for the Trigonometric Ratios 45o - 45o - 90o Triangles 1 30 2 2 2 1 60 2 1 1 1 1 = 45o 1 Nov 71:21 PM Nov 88:06 AM Determine the exact coordinates of P , Q , R and S. Q Angles in Standard Position • find the initial arm • find the terminal arm • rotate the terminal arm counterclockwise • mark 90, 180, 270 and 360 degrees y 4 3 R 2 S 1 x 4 3 2 1 0 1 2 3 4 1 2 3 • • • • 4 Nov 88:13 AM Example 1 • • • • approximate and mark 45 deg 135 deg 225 deg 315 deg approximate 130 deg 560 deg -130 deg -560 deg Nov 88:16 AM The Unit Circle and CAST a) Determine 3 positive angles co-terminal with 150o the primary ratios the reciprocal ratios b) Determine 3 negative anglesco-terminal with 150o c) Give a general expression for all angles co-terminal with 150o Nov 88:25 AM Nov 88:33 AM 1 01 trigonometric ratios of any angle in standard position.notebook Draw 135o and state the reference angle. Use special triangles and CAST to determine all 6 trigonometric ratios of 135o Draw -225o and state the reference angle. Use special triangles and CAST to determine all 6 trigonometric ratios of -225o Nov 88:49 AM Draw 330o and state the reference angle. Use special triangles and CAST to determine all 6 trigonometric ratios of 330o November 12, 2012 Nov 88:51 AM Draw -240o and state the reference angle. Use special triangles and CAST to determine all 6 trigonometric ratios of -240o Nov 88:52 AM Nov 88:52 AM Example 2 Draw 156o and state the reference angle. a) Use special triangles and CAST to determine all 6 trigonometric ratios of 510o Use the calculator to approximate all 6 trigonometric ratios of 156o Nov 88:54 AM Nov 88:47 AM 2 01 trigonometric ratios of any angle in standard position.notebook November 12, 2012 b) Use the calculator to approximate all 6 trigonometric ratios of -416o Circles of radius r and CAST the secondary ratios the primary ratios Nov 88:53 AM Example 3 Determine the exact values of all 6 ratios. Then determine the angle to the nearest tenth of a degree. What reference angle did you use? Nov 89:20 AM Determine the exact values of all 6 ratios. Then determine the angle to the nearest tenth of a degree. What reference angle did you use? (-8,-5) Nov 89:24 AM Nov 89:26 AM Determine the exact values of all 6 ratios. Then determine the angle to the nearest tenth of a degree. What reference angle did you use? What reference angle did you use? (3,-10) Nov 89:28 AM Nov 810:08 AM 3 01 trigonometric ratios of any angle in standard position.notebook What reference angle did you use? November 12, 2012 What reference angle did you use? Nov 810:14 AM Nov 810:15 AM Example 4 Example 4 Nov 89:54 AM Nov 810:06 AM like #3 page 474 Evaluate sec(-186o) in two ways. Nov 810:07 AM Nov 810:32 AM 4 01 trigonometric ratios of any angle in standard position.notebook November 12, 2012 like #5 page 475 like #4 page 474 Sketch 620o in standard position and identify the reference angle b) State the general formula for all angles co-terminal to the given angle. Nov 810:37 AM like #6 page 476 Nov 810:38 AM like #7 page 477 Complete this chart. Determine the exact values for the 6 ratios for -870o Nov 810:49 AM like #8 page 477 Nov 810:53 AM like #10 page 478 Determine the exact values of the ratios and find the angle to 1 decimal place. The point at the end of the terminal arm has coordinates P(-5,-11). State the reference angle. Nov 810:55 AM Nov 810:57 AM 5