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受欢迎的三角函数 >

sin(x/2)-cos(x/2)=0

解答

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

解答

x = \frac{π}{2} + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n

求解步骤

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

使用三角恒等式改写

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

在两边除以

cos (\frac{x}{2}), cos (\frac{x}{2}) \neq = 0

\frac{sin ( \frac{x}{2} ) - cos ( \frac{x}{2} )}{cos ( \frac{x}{2} )} = \frac{0}{cos ( \frac{x}{2} )}

化简

\frac{sin ( \frac{x}{2} )}{cos ( \frac{x}{2} )} - 1 = 0

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (\frac{x}{2}) - 1 = 0

tan (\frac{x}{2}) - 1 = 0

将

1

到右边

tan (\frac{x}{2}) - 1 = 0

两边加上

1

tan (\frac{x}{2}) - 1 + 1 = 0 + 1

化简

tan (\frac{x}{2}) = 1

tan (\frac{x}{2}) = 1

tan (\frac{x}{2}) = 1

的通解

tan (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

\frac{x}{2} = \frac{π}{4} + πn

\frac{x}{2} = \frac{π}{4} + πn

解

\frac{x}{2} = \frac{π}{4} + πn : x = \frac{π}{2} + 2 πn

\frac{x}{2} = \frac{π}{4} + πn

在两边乘以

2

\frac{x}{2} = \frac{π}{4} + πn

在两边乘以

2

\frac{2 x}{2} = 2 \cdot \frac{π}{4} + 2 πn

化简

\frac{2 x}{2} = 2 \cdot \frac{π}{4} + 2 πn

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

2 \cdot \frac{π}{4} + 2 πn : \frac{π}{2} + 2 πn

2 \cdot \frac{π}{4} + 2 πn

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{4}

约分:

2

= \frac{π}{2}

= \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

作图

流行的例子

2sin^2(x/3)=1,-pi<= ,x<= pi

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

sin (A) = 0.53

2sin(2x)=cos(2x)

2 sin (2 x) = cos (2 x)

0.428=cos(1.57*x-pi)

0.428 = cos (1.57 \cdot x - π)

solvefor t,y=cos(t)

so l v e f or t, y = cos (t)