1、求下列函數(shù)的定義域(1)根號(hào)下sin(cosx)(2)根號(hào)下cos(sinx)(3)lgsin2x+根號(hào)下16-x2

熱心網(wǎng)友

(1)根號(hào)下sin(cosx):== sin(cosx) = 0 === 1 = cosx = 0 因此, 定義域?yàn)? 2n*pi - pi/2 0 及: 16-x^2 = 0sin2x 0 == n*pi = 0 == -4 <= x <= 4因此: 定義域?yàn)? x = {(-pi,-pi/2),(0,pi/2),(pi,4]}

熱心網(wǎng)友

(1)依題意得sin(cosx),則2kπ≤cosx≤(2k+1)π,(k∈Z),又-1≤cosx≤1,與上解集相交得0≤cosx≤1,故2kπ-π/2≤x≤2kπ+π/2,,(k∈Z).(2)依題意得cos(sinx)≥0,則2kπ-π/2≤sinx≤2kπ+π/2,(k∈Z),又-1≤sinx≤1，與上解集相交得-1≤sinx≤1，故x∈R.(3)依題意得sin2x＞0且16-x^2≥0,即2kπ＜2x＜2kπ+π,(k∈Z)且-4≤x≤4,即kπ＜x＜kπ+π/2,(k∈Z)且-4≤x≤4,解得-π＜x＜-π/2或0＜x＜π/2或π＜x≤4.

熱心網(wǎng)友

如圖,不知有否做錯(cuò),

熱心網(wǎng)友

1 題 有0到90度