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受欢迎的三角函数 >

sin(5x)cos(x)-cos(5x)sin(x)=0

解答

sin (5 x) cos (x) - cos (5 x) sin (x) = 0

解答

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

+1

度数

x = 0^{\circ} + 9 0^{\circ} n, x = 4 5^{\circ} + 9 0^{\circ} n

求解步骤

sin (5 x) cos (x) - cos (5 x) sin (x) = 0

使用三角恒等式改写

sin (5 x) cos (x) - cos (5 x) sin (x)

使用角差恒等式:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (5 x - x)

sin (5 x - x) = 0

sin (5 x - x) = 0

的通解

sin (x)

周期表（周期为

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

5 x - x = 0 + 2 πn, 5 x - x = π + 2 πn

5 x - x = 0 + 2 πn, 5 x - x = π + 2 πn

解

5 x - x = 0 + 2 πn : x = \frac{πn}{2}

5 x - x = 0 + 2 πn

同类项相加:

5 x - x = 4 x

4 x = 0 + 2 πn

0 + 2 πn = 2 πn

4 x = 2 πn

两边除以

4

4 x = 2 πn

两边除以

4

\frac{4 x}{4} = \frac{2 πn}{4}

化简

x = \frac{πn}{2}

x = \frac{πn}{2}

解

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

5 x - x = π + 2 πn

同类项相加:

5 x - x = 4 x

4 x = π + 2 πn

两边除以

4

4 x = π + 2 πn

两边除以

4

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

化简

x = \frac{π}{4} + \frac{πn}{2}

x = \frac{π}{4} + \frac{πn}{2}

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

作图

流行的例子

2 sin (3 x + 1) + 1 = 2

2 sin (3 x + 1) + 1 = 1

sin (x) = 6946

sin(2x)-(sqrt(3))/2 =0,-2pi<= x<= 2pi

sin (2 x) - \frac{3}{2} = 0, - 2 π \leq x \leq 2 π

(sec(x)+tan(x))/(cot(x)+cos(x))=sec^2(x)

\frac{sec ( x ) + tan ( x )}{cot ( x ) + cos ( x )} = sec^{2} (x)