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受欢迎的三角函数 >

tan(x)sin(x)+sin(-x)=0,0<= x<= 2pi

解答

tan (x) sin (x) + sin (- x) = 0, 0 \leq x \leq 2 π

解答

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{5 π}{4}

+1

度数

x = 0^{\circ}, x = 18 0^{\circ}, x = 36 0^{\circ}, x = 4 5^{\circ}, x = 22 5^{\circ}

求解步骤

tan (x) sin (x) + sin (- x) = 0, 0 \leq x \leq 2 π

使用三角恒等式改写

tan (x) sin (x) + sin (- x) = 0

- sin (x) + sin (x) tan (x) = 0

- sin (x) + sin (x) tan (x) = 0

分解

- sin (x) + sin (x) tan (x) : sin (x) (tan (x) - 1)

- sin (x) + sin (x) tan (x)

因式分解出通项

sin (x)

= sin (x) (- 1 + tan (x))

sin (x) (tan (x) - 1) = 0

分别求解每个部分

sin (x) = 0 or tan (x) - 1 = 0

sin (x) = 0, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

sin (x) = 0, 0 \leq x \leq 2 π

sin (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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = 0, x = π, x = 2 π

tan (x) - 1 = 0, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{5 π}{4}

tan (x) - 1 = 0, 0 \leq x \leq 2 π

将

1

到右边

tan (x) - 1 = 0

两边加上

1

tan (x) - 1 + 1 = 0 + 1

化简

tan (x) = 1

tan (x) = 1

tan (x) = 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}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{π}{4}, x = \frac{5 π}{4}

合并所有解

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{5 π}{4}

作图

流行的例子

tan((2x)/3)+sqrt(3)=0

tan (\frac{2 x}{3}) + 3 = 0

cos(x+(3pi)/4)-cos(x-(3pi)/4)=0

cos (x + \frac{3 π}{4}) - cos (x - \frac{3 π}{4}) = 0

tan (x) = \frac{50}{100}

cos (x) = \frac{4}{6}

2cot^2(x)-5=sec^2(x)-tan^2(x)

2 cot^{2} (x) - 5 = sec^{2} (x) - tan^{2} (x)