高中数学-高考试题(上海交通大学 1931年三角函数方程)

问答题（1931年上海交通大学）

Find all the positive angles less than 360° which satisfy the equation:

cos2x+cosx+1=0

答案解析

暂无答案

讨论

高中数学

Homologous sides of two similar polygons have the ratio of 5 to 9 , the sum of the areas is 212 sq. ft. Find the area of each figure.

If two circles tangent at C and a common exterior tangent touches the circles in A and B, the angle ACB is a right angle.

Find the sum of the geometical series -2,,-1/3 to 6 terms.

Find the sum of the arithmetical series 49,44,39,… to 17 terms.

A motion picture film 120 feet long contains a certain number of individual pictures.If each picture were 0.1 of an inch shorter, the same film would contain 720 more pictures, how long is each picture?

Factor the following:4(a-b)²-12(a-b)(e+9e²)

Factor the following:4a-16b+4a+1.

Find the equation of the ruled surface whose generators are the system of the lines x-2y =4kx,k(x-2y)=4 and discuss the surface.

Find the equation of the sphere which passes through (1,5,-3),(-3,0,0) which center on the 3x+y+z=0,x+2y +1 = 0.

Find the equation of the plane passing through the line (x-x1)/a1 =(y-y1)/b1 =(z-z1)/c1 which is parallel to the (x-x2)/a2 =(y-y2)/b2 =(z-z2)/c2 .

三角函数

函数y=-xcos⁡x的部分图像是【】

已知函数y=1/2 cos2⁡x+/2 sin⁡xcos⁡x+1,x∈R.（I）当函数y取得最大值时，求自变量x的集合；（II）该函数的图像可由y=sin⁡x (x∈R)的图像经过怎样的平移和伸缩变换得到？

若sinθcosθ>0，则θ在【】

函数y=cos⁡x+1(-π≤x≤0)的反函数是【】

设x=sinα,且α∈[-π/6,5π/6]，则arccos⁡x的取值范围是________.

求函数y=(sinx+cosx)2+2cos2x的最小正周期.

下列区间中，函数f(x)=7sin⁡(x-π/6)单调递增的区间是【】

函数f(x)=sin x/3+cos x/3的最小正周期和最大值分别是【】

cos2 π/12 - cos2 5π/12=【】

已知函数f(x)=cosx-cos2x，则该函数【】

三角函数方程

若sin2x>cos2x，则x的取值范围是【】

函数y=cos2⁡x - 3cos⁡x + 2的最小值为【】

一个直角三角形三内角的正弦值成等比数列,其最小内角为【】

解方程：sinx+cosx-1=0

函数f(x)=cos⁡x+(x+1)sin⁡x+1在区间[0,2π]的最小值、最大值分别为【】

考虑下面2列，选择正确的选项【】列Ⅰ 列Ⅱ(Ⅰ) {x∈[-2π/3,2π/3]:cosx+sinx=1} (P)有2个元素(Ⅱ) {x∈[-5π/18,5π/18]:√3 tan3x=1} (Q)有3个元素(Ⅲ) {x∈[-6π/5,6π/5]:2cos2x=√3} (R)有4个元素(Ⅳ) {x∈[-7π/4,7π/4]:sinx-cosx=1} (S)有5个元素 (T)有6个元素

已知cosx=(1-(M+1)sin2x)/(1+(M-1)sin2x)，求x的值.

Find all the positive angles less than 380° which satisfy the equation sinx+sin2xsin3x = 0.

已知函数f(x)=cosωx-1(ω>0)在区间[0,2π]有且仅有3个零点, 则ω的取值范围是__________.

若函数 f(x) = sin(x + φ) + cosx 的最大值为 2, 则常数 φ 的一个取值为__________.