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受欢迎的三角函数 >

sin(30-x)+cos(x)=0

解答

sin (3 0^{\circ} - x) + cos (x) = 0

解答

x = 6 0^{\circ} + 18 0^{\circ} n

+1

弧度

x = \frac{π}{3} + πn

求解步骤

sin (3 0^{\circ} - x) + cos (x) = 0

使用三角恒等式改写

sin (3 0^{\circ} - x) + cos (x) = 0

使用三角恒等式改写

sin (3 0^{\circ} - x)

使用角差恒等式:

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

= sin (3 0^{\circ}) cos (x) - cos (3 0^{\circ}) sin (x)

化简

sin (3 0^{\circ}) cos (x) - cos (3 0^{\circ}) sin (x) : \frac{1}{2} cos (x) - \frac{3}{2} sin (x)

sin (3 0^{\circ}) cos (x) - cos (3 0^{\circ}) sin (x)

化简

sin (3 0^{\circ}) : \frac{1}{2}

sin (3 0^{\circ})

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2} cos (x) - cos (3 0^{\circ}) sin (x)

化简

cos (3 0^{\circ}) : \frac{3}{2}

cos (3 0^{\circ})

使用以下普通恒等式:

cos (3 0^{\circ}) = \frac{3}{2}

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{1}{2} cos (x) - \frac{3}{2} sin (x)

= \frac{1}{2} cos (x) - \frac{3}{2} sin (x)

\frac{1}{2} cos (x) - \frac{3}{2} sin (x) + cos (x) = 0

化简

\frac{1}{2} cos (x) - \frac{3}{2} sin (x) + cos (x) : \frac{3}{2} cos (x) - \frac{3}{2} sin (x)

\frac{1}{2} cos (x) - \frac{3}{2} sin (x) + cos (x)

同类项相加:

\frac{1}{2} cos (x) + cos (x) = \frac{3}{2} cos (x)

\frac{1}{2} cos (x) + cos (x)

因式分解出通项

cos (x)

= cos (x) (\frac{1}{2} + 1)

\frac{1}{2} + 1 = \frac{3}{2}

\frac{1}{2} + 1

将项转换为分式:

1 = \frac{1 \cdot 2}{2}

= \frac{1}{2} + \frac{1 \cdot 2}{2}

因为分母相等，所以合并分式:

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

= \frac{1 + 1 \cdot 2}{2}

1 + 1 \cdot 2 = 3

1 + 1 \cdot 2

数字相乘:

1 \cdot 2 = 2

= 1 + 2

数字相加:

1 + 2 = 3

= 3

= \frac{3}{2}

= \frac{3}{2} cos (x)

= \frac{3}{2} cos (x) - \frac{3}{2} sin (x)

\frac{3}{2} cos (x) - \frac{3}{2} sin (x) = 0

\frac{3}{2} cos (x) - \frac{3}{2} sin (x) = 0

化简

\frac{3}{2} cos (x) - \frac{3}{2} sin (x) : \frac{3 cos ( x ) - 3 sin ( x )}{2}

\frac{3}{2} cos (x) - \frac{3}{2} sin (x)

乘

\frac{3}{2} cos (x) : \frac{3 cos ( x )}{2}

\frac{3}{2} cos (x)

分式相乘:

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

= \frac{3 cos ( x )}{2}

= \frac{3 cos ( x )}{2} - \frac{3}{2} sin (x)

乘

\frac{3}{2} sin (x) : \frac{3 sin ( x )}{2}

\frac{3}{2} sin (x)

分式相乘:

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

= \frac{3 sin ( x )}{2}

= \frac{3 cos ( x )}{2} - \frac{3 sin ( x )}{2}

使用法则

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

= \frac{3 cos ( x ) - 3 sin ( x )}{2}

\frac{3 cos ( x ) - 3 sin ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 cos (x) - 3 sin (x) = 0

使用三角恒等式改写

3 cos (x) - 3 sin (x) = 0

在两边除以

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

\frac{3 cos ( x ) - 3 sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

化简

3 - \frac{3 sin ( x )}{cos ( x )} = 0

使用基本三角恒等式:

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

3 - 3 tan (x) = 0

3 - 3 tan (x) = 0

将

3

到右边

3 - 3 tan (x) = 0

两边减去

3

3 - 3 tan (x) - 3 = 0 - 3

化简

- 3 tan (x) = - 3

- 3 tan (x) = - 3

两边除以

- 3

- 3 tan (x) = - 3

两边除以

- 3

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

化简

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

\frac{- 3}{- 3}

使用分式法则:

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

= \frac{3}{3}

使用根式运算法则:

n a = a^{\frac{1}{n}}

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

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

使用指数法则:

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

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

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

数字相减:

1 - \frac{1}{2} = \frac{1}{2}

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

使用根式运算法则:

a^{\frac{1}{n}} = n a

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

= 3

tan (x) = 3

tan (x) = 3

tan (x) = 3

tan (x) = 3

的通解

tan (x)

周期表（周期为

18 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 6 0^{\circ} + 18 0^{\circ} n

x = 6 0^{\circ} + 18 0^{\circ} n

作图

流行的例子

tan (b x) = 5

sin(t+pi/4)= 1/2 ,pi<= t<= (7pi)/2

sin (t + \frac{π}{4}) = \frac{1}{2}, π \leq t \leq \frac{7 π}{2}

2cos^2(t)+7cos(t)+5=0

2 cos^{2} (t) + 7 cos (t) + 5 = 0

\frac{π}{6} = cos (2 t)

12cos^2(x)-cos(x)-1=0

12 cos^{2} (x) - cos (x) - 1 = 0