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受欢迎的三角函数 >

-2sqrt(2)=-2sec(x+150)

解答

- 22 = - 2 sec (x + 15 0^{\circ})

解答

x = 36 0^{\circ} n - 10 5^{\circ}, x = 36 0^{\circ} n + 16 5^{\circ}

+1

弧度

x = - \frac{7 π}{12} + 2 πn, x = \frac{11 π}{12} + 2 πn

求解步骤

- 22 = - 2 sec (x + 15 0^{\circ})

交换两边

- 2 sec (x + 15 0^{\circ}) = - 22

两边除以

- 2

- 2 sec (x + 15 0^{\circ}) = - 22

两边除以

- 2

\frac{- 2 sec ( x + 15 0 ^{\circ} )}{- 2} = \frac{- 2 2}{- 2}

化简

\frac{- 2 sec ( x + 15 0 ^{\circ} )}{- 2} = \frac{- 2 2}{- 2}

化简

\frac{- 2 sec ( x + 15 0 ^{\circ} )}{- 2} : sec (x + 15 0^{\circ})

\frac{- 2 sec ( x + 15 0 ^{\circ} )}{- 2}

使用分式法则:

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

= \frac{2 sec ( x + 15 0 ^{\circ} )}{2}

数字相除:

\frac{2}{2} = 1

= sec (x + 15 0^{\circ})

化简

\frac{- 2 2}{- 2} : 2

\frac{- 2 2}{- 2}

使用分式法则:

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

= \frac{2 2}{2}

数字相除:

\frac{2}{2} = 1

= 2

sec (x + 15 0^{\circ}) = 2

sec (x + 15 0^{\circ}) = 2

sec (x + 15 0^{\circ}) = 2

sec (x + 15 0^{\circ}) = 2

的通解

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x + 15 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n, x + 15 0^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

x + 15 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n, x + 15 0^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

解

x + 15 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n - 10 5^{\circ}

x + 15 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n

将

15 0^{\circ}

到右边

x + 15 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n

两边减去

15 0^{\circ}

x + 15 0^{\circ} - 15 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ}

化简

x + 15 0^{\circ} - 15 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ}

化简

x + 15 0^{\circ} - 15 0^{\circ} : x

x + 15 0^{\circ} - 15 0^{\circ}

同类项相加:

15 0^{\circ} - 15 0^{\circ} = 0

= x

化简

4 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ} : 36 0^{\circ} n - 10 5^{\circ}

4 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ}

对同类项分组

= 36 0^{\circ} n + 4 5^{\circ} - 15 0^{\circ}

4, 6

的最小公倍数:

12

4, 6

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

将每个因子乘以它在

4

或

6

中出现的最多次数

= 2 \cdot 2 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 = 12

= 12

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

12

对于

4 5^{\circ} :

将分母和分子乘以

3

4 5^{\circ} = \frac{18 0 ^{\circ} 3}{4 \cdot 3} = 4 5^{\circ}

对于

15 0^{\circ} :

将分母和分子乘以

2

15 0^{\circ} = \frac{90 0 ^{\circ} 2}{6 \cdot 2} = 15 0^{\circ}

= 4 5^{\circ} - 15 0^{\circ}

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{18 0 ^{\circ} 3 - 180 0 ^{\circ}}{12}

同类项相加:

54 0^{\circ} - 180 0^{\circ} = - 126 0^{\circ}

= \frac{- 126 0 ^{\circ}}{12}

使用分式法则:

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

= 36 0^{\circ} n - 10 5^{\circ}

x = 36 0^{\circ} n - 10 5^{\circ}

x = 36 0^{\circ} n - 10 5^{\circ}

x = 36 0^{\circ} n - 10 5^{\circ}

解

x + 15 0^{\circ} = 31 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 16 5^{\circ}

x + 15 0^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

将

15 0^{\circ}

到右边

x + 15 0^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

两边减去

15 0^{\circ}

x + 15 0^{\circ} - 15 0^{\circ} = 31 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ}

化简

x + 15 0^{\circ} - 15 0^{\circ} = 31 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ}

化简

x + 15 0^{\circ} - 15 0^{\circ} : x

x + 15 0^{\circ} - 15 0^{\circ}

同类项相加:

15 0^{\circ} - 15 0^{\circ} = 0

= x

化简

31 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ} : 36 0^{\circ} n + 16 5^{\circ}

31 5^{\circ} + 36 0^{\circ} n - 15 0^{\circ}

对同类项分组

= 36 0^{\circ} n + 31 5^{\circ} - 15 0^{\circ}

4, 6

的最小公倍数:

12

4, 6

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

将每个因子乘以它在

4

或

6

中出现的最多次数

= 2 \cdot 2 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 = 12

= 12

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

12

对于

31 5^{\circ} :

将分母和分子乘以

3

31 5^{\circ} = \frac{126 0 ^{\circ} 3}{4 \cdot 3} = 31 5^{\circ}

对于

15 0^{\circ} :

将分母和分子乘以

2

15 0^{\circ} = \frac{90 0 ^{\circ} 2}{6 \cdot 2} = 15 0^{\circ}

= 31 5^{\circ} - 15 0^{\circ}

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{378 0 ^{\circ} - 180 0 ^{\circ}}{12}

同类项相加:

378 0^{\circ} - 180 0^{\circ} = 198 0^{\circ}

= 36 0^{\circ} n + 16 5^{\circ}

x = 36 0^{\circ} n + 16 5^{\circ}

x = 36 0^{\circ} n + 16 5^{\circ}

x = 36 0^{\circ} n + 16 5^{\circ}

x = 36 0^{\circ} n - 10 5^{\circ}, x = 36 0^{\circ} n + 16 5^{\circ}

作图

流行的例子

9sin(θ)+sqrt(11)=0

9 sin (θ) + 11 = 0

(4sin(2x)+4cos(2x))^2=16

(4 sin (2 x) + 4 cos (2 x))^{2} = 16

2sec(x)tan(x)+sec^2(x)=0

2 sec (x) tan (x) + sec^{2} (x) = 0

sec^2(x)+4tan(x)=6

sec^{2} (x) + 4 tan (x) = 6

sin^2(θ)=4-2cos^2(θ)

sin^{2} (θ) = 4 - 2 cos^{2} (θ)