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受欢迎的 >

-sqrt(3)sin(x)=cos(x)

解答

- 3 sin (x) = cos (x)

解答

x = \frac{5 π}{6} + πn

+1

度数

x = 15 0^{\circ} + 18 0^{\circ} n

求解步骤

- 3 sin (x) = cos (x)

使用三角恒等式改写

- 3 sin (x) = cos (x)

在两边除以

cos (x), cos (x) \neq = 0

\frac{- 3 sin ( x )}{cos ( x )} = \frac{cos ( x )}{cos ( x )}

化简

- \frac{3 sin ( x )}{cos ( x )} = 1

使用基本三角恒等式:

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

- 3 tan (x) = 1

- 3 tan (x) = 1

两边除以

- 3

- 3 tan (x) = 1

两边除以

- 3

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

化简

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

化简

\frac{- 3 tan ( x )}{- 3} : tan (x)

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

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

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

约分:

3

= tan (x)

化简

\frac{1}{- 3} : - \frac{3}{3}

\frac{1}{- 3}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{3}

- \frac{1}{3}

有理化:

- \frac{3}{3}

- \frac{1}{3}

乘以共轭根式

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

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

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

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

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

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{5 π}{6} + πn

x = \frac{5 π}{6} + πn

流行的例子

2csc^2(x)=5-5cot(x)

2 csc^{2} (x) = 5 - 5 cot (x)

sin(x+0.5)=0.92,0<= x<= 2pi

sin (x + 0.5) = 0.92, 0 \leq x \leq 2 π

cos(4x)=0.8-0.6

cos (4 x) = 0.8 - 0.6

5cos^2(x)=4-3sin^2(x)

5 cos^{2} (x) = 4 - 3 sin^{2} (x)

(18cos(2θ)+2+cos(θ))/2 =0

\frac{18 cos ( 2 θ ) + 2 + cos ( θ )}{2} = 0