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 380° which satisfy the equation sinx+sin2xsin3x = 0.

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高中数学

Solve the following equation by taking the steps performed in srriving at Cardann formulas, but do not formulas themselves: x³ - 15x² - 33x +847= 0.

Six persons throw for a stake, which is to be won by the one who first throws head with a coin: if they throw in succession, find the chance of the fourth person.

Find the general term and the sum ofn terms of the series -3,-1,11,39,89,167.

Find the sum of n terms of the series whose nth term is 3(4n+4n²)-5n³.

If w is one of the imaginary cute roots of unity, show that the square of =hence show that the value of the determinant on the left is 3.

A man borrows $5000 at 4 percent compound interest, if the principal and interest are to be repaid by 10 equal instalments, find the amount of each instalment; having given 1g 1.04 =0.0170333 and lg675565=5.829667.

Find the maximum value of (5+x)(2+x)/(1-x).

Find the maximum value of (7-x)4 (2+x)6 when x lies between 7 and 2.

Resolve (1+52x+30x2-24x3)/(3x2-x-1)2 into partial fractions.

Factor the following expressions:x(y - z)³ + y(z -x)³ + z(x - y)³

三角函数

求证：(sinα+sinβ)/sin⁡(α+β)=cos((α-β)/2)/cos((α+β)/2)

计算：sin 4π/3∙cos 25π/6∙tg(-3π/4).

已知x+x-1=2cosθ，求证：xn+x-n=2cosnθ.

不查表求sin105°的值.

求sin⁡(2arcsin(⁡4/5))的值.

记函数f(x)=sin⁡(ωx+π/4)+b(ω>0)的最小正周期为T.若2/3 π<T<π，且y=f(x)的函数图像关于点(3π/2,2)中心对称，则f(π/2)=【】

函数f(x)=sin⁡(2x+φ)(0<φ<π)的图像以(2π/3,0)中心对称，则【】

设函数f(x)=sin⁡(ωx+π/3)在区间(0,π)恰有三个极值点、两个零点，则ω的取值范围是【】

将函数f(x)=sin⁡(ωx+π/3) (ω>0)的图像向左平移π/2个单位长度后得到曲线C，若C关于y轴对称，则ω的最小值是【】

记△ABC的内角A,B,C的对边分别为a,b,c，已知sin⁡Csin⁡( A-B)=sin⁡Bsin⁡(C-A)．（1）证明：2a2=b2+c2；（2）若a=5,cos⁡A=25/31，求△ABC的周长．

三角函数方程

求方程(sinx+cosx)2=1/2的解集.

求方程2sin(x+π/6)=1的解集.

方程4cos2x-4cosx+3=0的解集是【】

方程sinx-cosx=的解集是____________________.

方程sin2x=sinx在区间(0,2π)内的解的个数是【】

求方程 + sinx = 0在[0,2π)上的解.

满足sin⁡(x - π/4)≥1/2的x的集合是【】

方程sin4xcos5x=-cos4xsin5x的一个解是【】

若sin2x>cos2x，则x的取值范围是【】

函数y=cos2⁡x - 3cos⁡x + 2的最小值为【】