ࡱ> [@ bjbj44 (bViVic r r r  ]]]]4^ }_____wwwi}k}k}k}k}k}k}$~R2}r wuwww}__}a{a{a{wd._r _i}a{wi}a{ta{{r {_^ r]w{5|4}0}{xz{ r {`wwa{wwwww}} S ]Q{ ]TOPIC 7-6: TRIGONOMETRIC RATIOS IN RIGHT TRIANGLES TRIGONOMETRIC RATIOS: Ratios of the lengths of the sides of a right triangle (related to the acute angles) The three most common ratios are SINE, COSINE, & TANGENT.  EXAMPLE 1 Find sin A, cos A, tan A, sin B, cos B, and tan B. Express each ratio as a fraction.  EXAMPLE 2 Find sin S, cos S, tan S, sin E, cos E, and tan E. Express each ratio as a fraction.   You can use trigonometric tables to evaluate expressions involving trigonometric ratios. EXAMPLE 3 Find each value using the trig table attached. a) cos 41( = ____________ b) sin 78( = _____________ EXAMPLE 4 Find the missing measurement(s).  a) b) c) d)  TABLE OF TRIGONOMETRIC VALUES m(ASin ACos ATan Am(ASin ACos ATan A1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 450.0175 0.0349 0.0523 0.0698 0.0872 0.1045 0.1219 0.1392 0.1564 0.1736 0.1908 0.2079 0.2250 0.2419 0.2588 0.2756 0.2924 0.3090 0.3256 0.3420 0.3584 0.3746 0.3907 0.4067 0.4226 0.4384 0.4540 0.4695 0.4848 0.50 0.5150 0.5299 0.5466 0.5592 0.5736 0.5878 0.6018 0.6157 0.6293 0.6428 0.6561 0.6691 0.6820 0.6947 0.70710.9998 0.9994 0.9986 0.9976 0.9962 0.9945 0.9925 0.9903 0.9877 0.9848 0.9816 0.9781 0.9744 0.9703 0.9659 0.9613 0.9563 0.9511 0.9455 0.9397 0.9336 0.9272 0.9205 0.9135 0.9063 0.8988 0.8910 0.8829 0.8746 0.8660 0.8572 0.8480 0.8387 0.8290 0.8192 0.8090 0.7986 0.7880 0.7771 0.7660 0.7547 0.7431 0.7314 0.7193 0.70710.0175 0.0349 0.0524 0.0699 0.0875 0.1051 0.1228 0.1405 0.1584 0.1763 0.1944 0.2126 0.2309 0.2493 0.2679 0.2867 0.3057 0.3249 0.3443 0.3640 0.3839 0.4040 0.4245 0.4452 0.4663 0.4877 0.5095 0.5317 0.5543 0.5774 0.6009 0.6249 0.6494 0.6745 0.7002 0.7265 0.7536 0.7813 0.8098 0.8391 0.8693 0.9004 0.9325 0.9657 146 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 900.7193 0.7314 0.7431 0.7547 0.7660 0.7771 0.7880 0.7986 0.8090 0.8192 0.8290 0.8387 0.8480 0.8572 0.8660 0.8746 0.8829 0.8910 0.8988 0.9063 0.9135 0.9205 0.9272 0.9336 0.9397 0.9455 0.9511 0.9563 0.9613 0.9659 0.9703 0.9744 0.9781 0.9816 0.9848 0.9877 0.9903 0.9925 0.9945 0.9962 0.9976 0.9986 0.9994 0.9998 10.6947 0.6820 0.6691 0.6561 0.6428 0.6293 0.6157 0.6018 0.5878 0.5736 0.5592 0.5466 0.5299 0.5150 0.50 0.4848 0.4695 0.4540 0.4384 0.4226 0.4067 0.3907 0.3746 0.3584 0.3420 0.3256 0.3090 0.2924 0.2756 0.2588 0.2419 0.2250 0.2079 0.1908 0.1736 0.1564 0.1392 0.1219 0.1045 0.0872 0.0698 0.0523 0.0349 0.0175 01.0355 1.0724 1.1106 1.1504 1.1918 1.2349 1.2799 1.3270 1.3764 1.4281 1.4826 1.5399 1.6003 1.6643 1.7321 1.8040 1.8807 1.9626 2.0503 2.1445 2.2460 2.3559 2.4751 2.6051 2.7475 2.9042 3.0777 3.2709 3.4874 3.7321 4.0108 4.3315 4.7046 5.1446 5.6713 6.3138 7.1154 8.1443 9.5144 11.4301 14.3007 19.0811 28.6363 57.2900 Undefined TRIGONOMETRIC RATIOABBREVIATIONDEFINITION Sine  Cosine  Tangent  A B C 13 12 5 S M E 4 5 3 37( Equation:____________ x = ________ 53( x 13 21( 69( 9 x Equation:____________ x = ________ 50( 11 x y 54( 8 x y Equation:____________ x = _____________ Equation:____________ y = _____________ Equation:____________ x = _____________ Equation:____________ y = _____________ +GHI\]^  G óóálbD3 h=h=CJ OJQJ^JaJ :jh=hB5CJ OJQJU\^JaJ mHnHuh=OJQJ^J&jh YOJQJU^JmHnHu(hbahba56CJ OJQJ\]^JhbaCJ OJQJ^J"hba56CJ OJQJ\]^Jh Y5CJ OJQJ\]^J%h Yhba5CJ OJQJ\]^JhbaCJ OJQJh]jCJ OJQJhbahbaCJ OJQJhbahbaCJ +HI       gdbagdbac  H        " { dgd=gd=gd=gdbaG H p   ! 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