函數(shù)y=(57x-56cosx)(58x+44sinx)的圖像示意圖主要內(nèi)容：本文根據(jù)三角正弦函數(shù)和余弦函數(shù)的周期性，并通過描點(diǎn)法，詳細(xì)介紹函數(shù)y=(57x-56cosx)(58x+44sinx)的圖像示意圖畫法步驟。函數(shù)的定義域：根據(jù)本題涉及的函數(shù)及其特征，為一次函數(shù)和三角函數(shù)和差的乘積，可知自變量x可以取任意實(shí)數(shù)，所以：函數(shù)y=(57x-56cosx)(58x+44sinx)的定義域?yàn)椋?-∞，+∞)。函數(shù)描點(diǎn)原則：由于三角函數(shù)具有周期性，本題用描點(diǎn)法畫函數(shù)y=(57x-56cosx)(58x+44sinx)的圖像。考慮周期性，本例需畫出在區(qū)間[-4π，4π]上的圖像示意圖，故取點(diǎn)原則為間隔1/4個(gè)周期進(jìn)行取點(diǎn)。函數(shù)特征點(diǎn)圖表：x-4π-3.75π-3.5π-3.25π-3π-2.75π57x-56cosx-772.3-711.1-626.7-542.4-481.2-452.858x+44sinx-728.8-652.2-593.7-561.1-546.6-532.2y562852463779372072304341263024240980x-2.5π-2.25π-2π-1.75π-1.5π-1.25π57x-56cosx-447.7-442.5-414.1-353.0-353.0-184.258x+44sinx-499.5-441.1-364.4-287.8-229.3-196.7y2236261951871508981015938094336232x-π-0.75π-0.5π-0.25π00.25π57x-56cosx-123.1-94.7-89.5-84.4-565.258x+44sinx-182.2-167.8-135.1-76.7076.7y22429158911209164730399x0.5π0.75ππ1.25π1.5π1.75π57x-56cosx89.5173.9235.1263.4268.6273.858x+44sinx135.1167.8182.2196.7229.3287.8y120912918042835518116159078800x2π2.25π2.5π2.75π3π3.25π57x-56cosx302.1363.3447.7532.0593.2621.658x+44sinx364.4441.1499.5532.2546.6561.1y110085160252223626283130324243348780x3.53.75π4π57x-56cosx626.7631.9660.358x+44sinx593.7652.2728.8y372072412125481227函數(shù)圖像示意圖：y=(57x-56cosx)(58x+44sinx)y (-4π,562852)(4π,481227)(3.5π,372072)(3π,324243)(-3.25π,304341)(-3π,263024)(-2.5π,223626)(2π,110085)