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受欢迎的三角函数 >

3tan^2(x)-1=0,0<= x<= 2pi

解答

3 tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

解答

x = \frac{π}{6}, x = \frac{7 π}{6}, x = \frac{5 π}{6}, x = \frac{11 π}{6}

+1

度数

x = 3 0^{\circ}, x = 21 0^{\circ}, x = 15 0^{\circ}, x = 33 0^{\circ}

求解步骤

3 tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

用替代法求解

3 tan^{2} (x) - 1 = 0

令

: tan (x) = u

3 u^{2} - 1 = 0

3 u^{2} - 1 = 0 : u = \frac{1}{3}, u = - \frac{1}{3}

3 u^{2} - 1 = 0

将

1

到右边

3 u^{2} - 1 = 0

两边加上

1

3 u^{2} - 1 + 1 = 0 + 1

化简

3 u^{2} = 1

3 u^{2} = 1

两边除以

3

3 u^{2} = 1

两边除以

3

\frac{3 u ^{2}}{3} = \frac{1}{3}

化简

u^{2} = \frac{1}{3}

u^{2} = \frac{1}{3}

对于

x^{2} = f (a)

解为

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

u = \frac{1}{3}, u = - \frac{1}{3}

u = tan (x)

代回

tan (x) = \frac{1}{3}, tan (x) = - \frac{1}{3}

tan (x) = \frac{1}{3}, tan (x) = - \frac{1}{3}

tan (x) = \frac{1}{3}, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{7 π}{6}

tan (x) = \frac{1}{3}, 0 \leq x \leq 2 π

使用反三角函数性质

tan (x) = \frac{1}{3}

tan (x) = \frac{1}{3}

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{1}{3}) + πn

x = arctan (\frac{1}{3}) + πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{π}{6}, x = \frac{7 π}{6}

tan (x) = - \frac{1}{3}, 0 \leq x \leq 2 π : x = \frac{5 π}{6}, x = \frac{11 π}{6}

tan (x) = - \frac{1}{3}, 0 \leq x \leq 2 π

使用反三角函数性质

tan (x) = - \frac{1}{3}

tan (x) = - \frac{1}{3}

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{1}{3}) + πn

x = arctan (- \frac{1}{3}) + πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{5 π}{6}, x = \frac{11 π}{6}

合并所有解

x = \frac{π}{6}, x = \frac{7 π}{6}, x = \frac{5 π}{6}, x = \frac{11 π}{6}

作图

流行的例子

sin(2x)=4cos(x)

sin (2 x) = 4 cos (x)

sqrt(3)tan(2x)-1=0

3 tan (2 x) - 1 = 0

cos (2 x + π) = 0

csc (θ) = - \frac{5}{4}

2 - sec^{2} (x) = 0