三角函数的诱导公式是什么
.诱导公式 sin(-a)=-sin(a) cos(-a)=cos(a) sin(π2-a)=cos(a) cos(π2-a)=sin(a) sin(π2+a)=cos(a) cos(π2+a)=-sin(a) sin(π-a)=sin(a) cos(π-a)=-cos(a) sin(π+a)=-sin(a) cos(π+a)=-cos(a) tgA=tanA=sinAcosA 2.两角和与差的三角函数 sin(a+b)=sin(a)cos(b)+cos(α)sin(b) cos(a+b)=cos(a)cos(b)-sin(a)sin(b) sin(a-b)=sin(a)cos(b)-cos(a)sin(b) cos(a-b)=cos(a)cos(b)+sin(a)sin(b) tan(a+b)=tan(a)+tan(b)1-tan(a)tan(b) tan(a-b)=tan(a)-tan(b)1+tan(a)tan(b) 3.和差化积公式 sin(a)+sin(b)=2sin(a+b2)cos(a-b2) sin(a)?sin(b)=2cos(a+b2)sin(a-b2) cos(a)+cos(b)=2cos(a+b2)cos(a-b2) cos(a)-cos(b)=-2sin(a+b2)sin(a-b2) 4.积化和差公式 (上面公式反过来就得到了) sin(a)sin(b)=-12 [cos(a+b)-cos(a-b)] cos(a)cos(b)=12 [cos(a+b)+cos(a-b)] sin(a)cos(b)=12 [sin(a+b)+sin(a-b)] 5.二倍角公式 sin(2a)=2sin(a)cos(a) cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a) 6.半角公式 sin2(a2)=1-cos(a)2 cos2(a2)=1+cos(a)2 tan(a2)=1-cos(a)sin(a)=sina1+cos(a) 7.万能公式 sin(a)=2tan(a2)1+tan2(a2) cos(a)=1-tan2(a2)1+tan2(a2) tan(a)=2tan(a2)1-tan2(a2) 8.其它公式(推导出来的 ) a sin(a)+b cos(a)=a2+b2sin(a+c) 其中 tan(c)=ba a sin(a)-b cos(a)=a2+b2cos(a-c) 其中 tan(c)=ab 1+sin(a)=(sin(a2)+cos(a2))2 1-sin(a)=(sin(a2)-cos(a2))2 其他非重点 csc(a)=1sin(a) sec(a)=1cos(a)绛旓細tan(蟺-x)=-tanx 鍘熺悊锛涓夎鍑芥暟鍊间腑锛屾寮︿竴浜岃薄闄愪负姝ｏ紝浣欏鸡涓鍥涜薄闄愪负姝ｏ紝姝ｅ垏涓涓夎薄闄愪负姝ｏ紙缁堣竟锛(5)sin(蟺/2+x)=cosx cos(蟺/2+x)=-sinx tan(蟺/2+x)=-cotx (6)sin(蟺/2-x)=cosx cos(蟺/2-x)=sinx tan(蟺/2-x)=cotx (7)灞曞紑鍏紡 sin(3蟺/2+x)=sin(蟺+蟺/2+...
绛旓細璇卞鍏紡鏄寚涓夎鍑芥暟涓紝鍒╃敤鍛ㄦ湡鎬у皢瑙掑害姣旇緝澶х殑涓夎鍑芥暟锛岃浆鎹负瑙掑害姣旇緝灏忕殑涓夎鍑芥暟鐨勫叕寮銆 璇卞鍏紡鏈夊叚缁勶紝鍏54涓傚叕寮忎竴 缁堣竟鐩稿悓鐨勮鐨勫悓涓涓夎鍑芥暟鐨勫肩浉绛夈傝伪涓轰换鎰忛攼瑙掞紝瑙掑害鍒朵笅鐨勮鐨勮〃绀猴細sin (伪+k路360掳)=sin伪锛坘鈭圸锛. cos(伪+k路360掳)=cos伪锛坘鈭圸锛.tan (...
绛旓細tan(a2)=1-cos(a)sin(a)=sina1+cos(a)7.涓囪兘鍏紡 sin(a)=2tan(a2)1+tan2(a2)cos(a)=1-tan2(a2)1+tan2(a2)tan(a)=2tan(a2)1-tan2(a2)8.鍏跺畠鍏紡(鎺ㄥ鍑烘潵鐨 )a⋅sin(a)+b⋅cos(a)=a2+b2sin(a+c) 鍏朵腑 tan(c)=ba a⋅sin(a)-b⋅cos(a...
绛旓細涓夎鍑芥暟璇卞鍏紡锛氫笁瑙掑嚱鏁扮殑鍩烘湰鍏紡锛1銆佸叕寮忎竴锛氫换鎰忚伪涓-伪鐨勪笁瑙掑嚱鏁板间箣闂寸殑鍏崇郴锛歴in锛堬紞伪锛=锛峴in伪cos锛堬紞伪锛=cos伪tan锛堬紞伪锛=锛峵an伪cot锛堬紞伪锛=锛峜ot伪 2銆佸叕寮忎簩锛歴in锛埾+伪锛=鈥攕in伪cos锛埾+伪锛=锛峜os伪tan锛埾+伪锛=tan伪cot锛埾+伪锛=cot伪 3銆佸叕寮忎笁锛氬埄鐢...
绛旓細cos(蟺锛嵨)=锛峜os伪銆傝繖鏄瀵煎叕寮忋備篃鍙互鍒╃敤鍜岃鍏紡锛歝os(伪-尾)=cos伪路cos尾+sin伪路sin尾锛屾帹瀵硷細cos(蟺锛嵨)=cos蟺cos伪+sin蟺sin伪=-cos伪銆傚埄鐢ㄥ叕寮忎簩鍜屽叕寮忎笁鍙互寰楀埌蟺-伪涓幬辩殑涓夎鍑芥暟鍊间箣闂寸殑鍏崇郴锛歴in(蟺锛嵨)=sin伪 cos(蟺锛嵨)=锛峜os伪 tan(蟺锛嵨)=锛峵an伪 cot...
绛旓細璇卞鍏紡涓夎鍑芥暟鍩烘湰鍏紡濡備笅锛歴in锛2k蟺+伪锛=sin伪锛坘鈭圸锛塩os锛2k蟺+伪锛=cos伪锛坘鈭圸锛塼an锛2k蟺+伪锛=tan伪锛坘鈭圸锛塩ot锛2k蟺+伪锛=cot伪锛坘鈭圸锛夎瀵煎叕寮忓彛璇鈥滃鍙樺伓涓嶅彉锛岀鍙风湅璞￠檺鈥濇剰涔夛細k脳蟺/2卤a锛坘鈭圸锛夌殑涓夎鍑芥暟鍊硷細锛1锛夊綋k涓哄伓鏁版椂锛岀瓑浜幬辩殑鍚屽悕涓夎鍑芥暟鍊硷紝...
绛旓細甯哥敤鐨勪笁瑙掑嚱鏁璇卞鍏紡鏈変互涓嬪嚑缁:鍏紡1 :璁綼涓轰换鎰忚,缁堣竟鐩稿悓鐨勮鐨勫悓- -涓夎鍑芥暟鐨鍊肩浉绛:sin ( 2k蟺+a) = sina cos ( 2k蟺+a) =Cosa tan ( 2k蟺+a) = tana cot ( 2k蟺+a) = cota 鍏紡浜:璁綼涓轰换鎰忚, 蟺+a鐨勪笁瑙掑嚱鏁板间笌x鐨勪笁瑙掑嚱鏁板间箣闂寸殑鍏崇郴:sin(蟺+a) = - sina...
绛旓細璇卞鍏紡鏄鎸囦笁瑙掑嚱鏁颁腑灏嗚搴︽瘮杈冨ぇ鐨勪笁瑙掑嚱鏁板埄鐢ㄨ鐨勫懆鏈熸э紝杞崲涓鸿搴︽瘮杈冨皬鐨涓夎鍑芥暟鐨鍏紡銆 璇卞鍏紡鏈夊叚缁勫叡54涓傚叕寮忎竴 璁疚变负浠绘剰瑙掞紝缁堣竟鐩稿悓鐨勮鐨勫悓涓涓夎鍑芥暟鐨勫肩浉绛夛細瀵逛簬x杞存鍗婅酱涓鸿捣鐐硅酱鑰岃█ 寮у害鍒朵笅鐨勮鐨勮〃绀猴細sin锛2k蟺+伪锛=sin伪 锛坘鈭圸锛塩os锛2k蟺+伪锛=cos伪 锛...
绛旓細sin锛埾/2-a锛=cosa銆傚熀鏈璇卞鍏紡銆傚垎鏋愯繃绋嬪涓嬶細鐢讳竴涓洿瑙涓夎褰紝纭畾涓涓攼瑙掓槸a锛屽垯锛宑osa鏄痑鐨勪复杈规瘮鏂滆竟锛岄偅涔堝彟涓涓攼瑙掑氨鏄/2-a锛屽浜庨偅涓鏉ヨ锛屽氨鏄杈规瘮鏂滆竟锛屽氨鏄寮︿簡銆
绛旓細涓夎鍑芥暟璇卞鍏紡鏄鏁板涓噸瑕佺殑杈呭姪宸ュ叿锛屽畠鎻忚堪浜嗕笉鍚岃搴︿笅涓夎鍑芥暟鍊间箣闂寸殑鍏崇郴銆備互涓嬫槸鍑犱釜鍩烘湰鐨勮瀵煎叕寮:鍏紡涓锛氬浜庝换鎰忚伪锛屾墍鏈変笌伪缁堣竟鐩稿悓鐨勮锛屽叾涓夎鍑芥暟鍊兼亽绛夛紝濡傦細sin(2k蟺+伪) = sin伪, cos(2k蟺+伪) = cos伪, tan(2k蟺+伪) = tan伪, cot(2k蟺+伪) = cot伪, 鍏朵腑k...
