已知tana=½，tanB=⅓，求tan2a和tan(a-B)
\u5df2\u77e5(tanA+tanB)=3,tan(B-\u03c0/4)=2,\u6c42tan2A\u7684\u503ctan(B-\u03c0/4)=[tanB-tan(\u03c0/4)]/[1+tanB*tan(\u03c0/4)]=2\uff0c\u6240\u4ee5tanB=-3\uff0c\u56e0\u4e3a(tanA+tanB)=3\uff0c\u6240\u4ee5tanA=6\uff0c\u6240\u4ee5tan2A=2tanA/\uff081-\uff08tanA\uff09^2\uff09=-12/35
tan2a=tan[(a+b)+(a-b)]=(2/5+1/4)/(1-2/5\u00d71/4)=13/18
tan2a=(2tana)/(1-tan²a)=13/18 \u89e3\u65b9\u7a0b\u53ef\u5f97tana,\u6570\u636e\u7e41\uff0c\u6709\u8bef?
tanb=tan[(a+b)-a]==[tan(a+b)-tana]/[1+tan(a+b)tana]
\u5c06tan(a+b)\uff0ctana\u4ee3\u5165\u5373\u5f97tanb
套基本公式即可。
tan2a=2tana/(1-tan²a)
=(2×0.5)/(1-0.5²)=4/3
tan(a-B)=(tana-tanB)/(1+tanatanB)=(0.5-1/3)/(1+0.5*1/3)=1/7
绛旓細鏍规嵁涓囪兘鍏紡鍙煡锛宸茬煡tana =2 sin2伪=2tan伪/锛1+tan²伪锛=4/5 cos2伪=锛1-tan²伪锛/锛1+tan²伪锛=-3/5 tan2伪=2tan伪/锛1-tan²伪锛=-4/3
绛旓細tana=sina/cosa=鈭3 sina=鈭3cosa sin²a=3cos²a 浠ｅ叆鎭掔瓑寮弒in²a+cos²a=1 鍒檆os²a=1/4 sina=鈭3cosa 鎵浠 cosa=-1/2,sina=-鈭3/2 cosa=1/2,sina=鈭3/2
绛旓細sina/cosa=tana=1/2 cosa=2sina cos²a=4sin²a 浠ｅ叆鎭掔瓑寮弒in²a+cos²a=1 鎵浠in²a=1/5,cos²=4/5 鎵浠ュ師寮=9
绛旓細tana=-鈭3 伪鏈夊彲鑳芥槸绗簩璞￠檺瑙掓垨绗洓璞￠檺瑙 伪涓虹浜岃薄闄愯鏃讹細sin伪=-tan伪/鈭(1+tan²伪)=鈭3/2 cos伪=-1/鈭(1+tan²伪)=-1/2 cot伪=1/tan伪=-鈭3/3 伪涓虹鍥涜薄闄愯鏃讹細sin伪=tan伪/鈭(1+tan²伪)=-鈭3/2 cos伪=1/鈭(1+tan²伪)=1/2 co...
绛旓細涓虹畝渚 sina=s,cosa=c.s/c=tana=-1/2 s²+c²=1 鑱旂珛涓婇潰涓ゅ紡瑙ｅ緱涓ょ粍瑙 s=璐熺殑鏍瑰彿涓嬩簲鍒嗕箣涓,c=鏍瑰彿涓嬩簲鍒嗕箣鍥 鎴 s=鏍瑰彿涓嬩簲鍒嗕箣涓,c=璐熺殑鏍瑰彿涓嬩簲鍒嗕箣鍥
绛旓細tana = 鈭3 (蟺 < a < 3蟺/2)鎵浠 a = 4蟺/3 鎵浠 cos a = -1/2 , sin a = -鈭3/2 鎵浠 cos a-sin a = (鈭3 - 1)/2
绛旓細tan(伪+尾)=(tan伪+tan尾)/(1-tan伪路tan尾)=(2+3)/(1-2*3)=-1 鍙堝洜涓篴銆佄插潎涓洪攼瑙 鎵浠+尾=135掳
绛旓細tan A=3.748 A=arc tan 3.748 =75.0609713掳 =75掳(0.0609713*60)'=75掳3.658278'=75掳3'(0.658278*60)"=75掳3'39.5"
绛旓細鐢讳竴涓洿瑙掍笁瑙掑舰锛岃鐭殑鐩磋杈逛负1锛岄暱鐨勭洿瑙掕竟涓3锛岃繖鏍tanA灏变负1/3浜嗐傜敤鍕捐偂瀹氬緥绠楀嚭鏂滆竟涓烘牴鍙10锛屾墍浠inA灏辨槸1/鏍瑰彿10
绛旓細鐢宸茬煡鍙緱锛tana=sina/cosa=2,閭ｄ箞锛歴ina=2cosa锛屽嵆cosa=(sina)/2 鎵浠ワ細(sina+cosa)/(sina-cosa)=(2cosa+cosa)/(2cosa-cosa)=3 鍙坰in²a+cos²a=1锛岄偅涔堬細sin²a+ (1/4)sin²a=1 (5/4)sin²a=1 sin²a=4/5 鍥犱负a鈭堬紙0锛屜/2锛夛紝鎵浠ワ細...
