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受欢迎的三角函数 >

sec(θ)-sqrt(2)tan(θ)=0

解答

sec (θ) - 2 tan (θ) = 0

解答

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

+1

度数

θ = 4 5^{\circ} + 36 0^{\circ} n, θ = 13 5^{\circ} + 36 0^{\circ} n

求解步骤

sec (θ) - 2 tan (θ) = 0

用 sin, cos 表示

sec (θ) - 2 tan (θ)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( θ )} - 2 tan (θ)

使用基本三角恒等式:

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

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

化简

\frac{1}{cos ( θ )} - 2 \frac{sin ( θ )}{cos ( θ )} : \frac{1 - 2 sin ( θ )}{cos ( θ )}

\frac{1}{cos ( θ )} - 2 \frac{sin ( θ )}{cos ( θ )}

乘

2 \frac{sin ( θ )}{cos ( θ )} : \frac{2 sin ( θ )}{cos ( θ )}

2 \frac{sin ( θ )}{cos ( θ )}

分式相乘:

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

= \frac{sin ( θ ) 2}{cos ( θ )}

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

使用法则

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

= \frac{1 - 2 sin ( θ )}{cos ( θ )}

= \frac{1 - 2 sin ( θ )}{cos ( θ )}

\frac{1 - sin ( θ ) 2}{cos ( θ )} = 0

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

1 - sin (θ) 2 = 0

将

1

到右边

1 - sin (θ) 2 = 0

两边减去

1

1 - sin (θ) 2 - 1 = 0 - 1

化简

- sin (θ) 2 = - 1

- sin (θ) 2 = - 1

两边除以

- 2

- sin (θ) 2 = - 1

两边除以

- 2

\frac{- sin ( θ ) 2}{- 2} = \frac{- 1}{- 2}

化简

\frac{- sin ( θ ) 2}{- 2} = \frac{- 1}{- 2}

化简

\frac{- sin ( θ ) 2}{- 2} : sin (θ)

\frac{- sin ( θ ) 2}{- 2}

使用分式法则:

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

= \frac{sin ( θ ) 2}{2}

约分:

2

= sin (θ)

化简

\frac{- 1}{- 2} : \frac{2}{2}

\frac{- 1}{- 2}

使用分式法则:

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

= \frac{1}{2}

\frac{1}{2}

有理化:

\frac{2}{2}

\frac{1}{2}

乘以共轭根式

\frac{2}{2}

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

1 \cdot 2 = 2

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{2}{2}

= \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

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}

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

作图

流行的例子

2sin(x-pi/3)=-sqrt(2)

2 sin (x - \frac{π}{3}) = - 2

3sin(θ)=1+cos(θ)

3 sin (θ) = 1 + cos (θ)

sqrt(2)sin(x)-sqrt(2)cos(x)=2

2 sin (x) - 2 cos (x) = 2

tan (x) = \frac{9}{12}

cos (x) = \frac{24}{25}