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受欢迎的三角函数 >

solvefor x,sin^2(x)=((1-cos(y)))/2

解答

求解

x, sin^{2} (x) = \frac{( 1 - cos ( y ) )}{2}

解答

x = arcsin (\frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn, x = arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (\frac{1 - cos ( y )}{2}) + 2 πn

求解步骤

sin^{2} (x) = \frac{( 1 - cos ( y ) )}{2}

用替代法求解

sin^{2} (x) = \frac{1 - cos ( y )}{2}

令

: sin (x) = u

u^{2} = \frac{1 - cos ( y )}{2}

u^{2} = \frac{1 - cos ( y )}{2} : u = \frac{1 - cos ( y )}{2}, u = - \frac{1 - cos ( y )}{2}

u^{2} = \frac{1 - cos ( y )}{2}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{1 - cos ( y )}{2}, u = - \frac{1 - cos ( y )}{2}

u = sin (x)

代回

sin (x) = \frac{1 - cos ( y )}{2}, sin (x) = - \frac{1 - cos ( y )}{2}

sin (x) = \frac{1 - cos ( y )}{2}, sin (x) = - \frac{1 - cos ( y )}{2}

sin (x) = \frac{1 - cos ( y )}{2} : x = arcsin (\frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn

sin (x) = \frac{1 - cos ( y )}{2}

使用反三角函数性质

sin (x) = \frac{1 - cos ( y )}{2}

sin (x) = \frac{1 - cos ( y )}{2}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (\frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn

x = arcsin (\frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn

sin (x) = - \frac{1 - cos ( y )}{2} : x = arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (\frac{1 - cos ( y )}{2}) + 2 πn

sin (x) = - \frac{1 - cos ( y )}{2}

使用反三角函数性质

sin (x) = - \frac{1 - cos ( y )}{2}

sin (x) = - \frac{1 - cos ( y )}{2}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (\frac{1 - cos ( y )}{2}) + 2 πn

x = arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (\frac{1 - cos ( y )}{2}) + 2 πn

合并所有解

x = arcsin (\frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn, x = arcsin (- \frac{1 - cos ( y )}{2}) + 2 πn, x = π + arcsin (\frac{1 - cos ( y )}{2}) + 2 πn

作图

流行的例子

sin(x)+sin^2(x)+cos(x)+cos^2(x)=0

sin (x) + sin^{2} (x) + cos (x) + cos^{2} (x) = 0

4cos^2(x)-4sin(x)-1=0

4 cos^{2} (x) - 4 sin (x) - 1 = 0

cos^2(x)+1=-2cos(x)

cos^{2} (x) + 1 = - 2 cos (x)

sin^3(x)-2sin(x)=0

sin^{3} (x) - 2 sin (x) = 0

2cos^3(x)=cot^3(x)

2 cos^{3} (x) = cot^{3} (x)