三角函数知识归纳总结

基本函数正弦函数余弦函数正切函数余切函数正割函数余割函数英文sinecosinetangentcotangentsecantcosecant缩写sincostancotseccsc表达式a/cb/ca/bb/ac/bc/a语言描述∠A 的对边比斜边∠A 的邻边比斜边∠A 的对边比邻边∠A 的邻边比对边∠A 的斜边比邻边∠A 的斜边比对边注：正切函数、余切函数曾被写作 tg、ctg，现已不用这种写法。特殊角角度0°15°30°45°60°90°120°135°150°180°270°弧度0π/12π/6π/4π/3π/22π/33π/45π/6π3π/2sin 值0[(√6)-(√2)]/41/2(√2)/2(√3)/21(√3)/2(√2)/21/20-1cos 值1[(√6)+(√2)]/4(√3)/2(√2)/21/20-1/2-(√2)/2-(√3)/2-10tan 值02-√3（√3）/31√3/-√3-1-(√3)/30/cot 值/2+√3√31(√3)/30-(√3)/3-1-√3/0几何性质函数对称轴对称中心图象y=sin xx=kπ+π/2(k∈Z)(kπ,0)(k∈Z)正弦函数y=cos xx=kπ(k∈Z)(kπ+π/2,0)(k∈Z)余弦函数y=tan x无(kπ/2+π/2,0)(k∈Z)正切函数y=cot x无(kπ/2,0)(k∈Z)余切函数y=sec xx=kπ(k∈Z)(kπ+π/2,0)(k∈Z)y=csc xx=kπ+π/2(k∈Z)(kπ,0)(k∈Z)诱导公式公式一sin(2kπ+α)=sin αcos(2kπ+α)=cos αtan(2kπ+α)=tan αcot(2kπ+α)=cot αsec(2kπ+α)=sec αcsc(2kπ+α)=csc α公式三sin(-α)=-sin αcos(-α)=cos αtan(-α)=-tan αcot(-α)=-cot αsec(-α)=sec αcsc(-α)=-csc α公式五sin(α-π)=-sin αcos(α-π)=-cos αtan(α-π)=tan αcot(α-π)=cot αsec(α-π)=-sec αcsc(α-π)=-csc α公式七sin(π/2+α)=cosαcos(π/2+α)=−sinαtan(π/2+α)=-cotαcot(π/2+α)=-tanαsec(π/2+α)=-cscαcsc(π/2+α)=secα公式九sin(3π/2+α)=-cosαcos(3π/2+α)=sinαtan(3π/2+α)=-cotαcot(3π/2+α)=-tanαsec(3π/2+α)=cscαcsc(3π/2+α)=-secα公式十sin(3π/2-α)=-cosαcos(3π/2-α)=-sinαtan(3π/2-α)=cotαcot(3π/2-α)=tanαsec(3π/2-α)=-cscαcsc(3π/2-α)=-secα公式八sin(π/2-α)=cosαcos(π/2-α)=sinαtan(π/2-α)=cotαcot(π/2-α)=tanαsec(π/2-α)=cscαcsc(π/2-α)=secα公式六sin(2π-α)=-sin αcos(2π-α)=cos αtan(2π-α)=-tan αcot(2π-α)=-cot αsec(2π-α)=sec αcsc(2π-α)=-csc α公式四sin(π-α)=sin αcos(π-α)=-cos αtan(π-α)=-tan αcot(π-α)=-cot αsec(π-α)=-sec αcsc(π-α)=csc α公式二sin(π+α)=-sin...