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受欢迎的三角函数 >

2tan(x)=sec(x)

解答

2 tan (x) = sec (x)

解答

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

+1

度数

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

求解步骤

2 tan (x) = sec (x)

两边减去

sec (x)

2 tan (x) - sec (x) = 0

用 sin, cos 表示

- sec (x) + 2 tan (x)

使用基本三角恒等式:

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

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

使用基本三角恒等式:

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

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

化简

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

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

乘

2 \cdot \frac{sin ( x )}{cos ( x )} : \frac{2 sin ( x )}{cos ( x )}

2 \cdot \frac{sin ( x )}{cos ( x )}

分式相乘:

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

= \frac{sin ( x ) \cdot 2}{cos ( x )}

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

使用法则

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

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

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

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

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

- 1 + 2 sin (x) = 0

将

1

到右边

- 1 + 2 sin (x) = 0

两边加上

1

- 1 + 2 sin (x) + 1 = 0 + 1

化简

2 sin (x) = 1

2 sin (x) = 1

两边除以

2

2 sin (x) = 1

两边除以

2

\frac{2 sin ( x )}{2} = \frac{1}{2}

化简

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{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}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

作图

流行的例子

cos (x) = 2 π

sin(6x)+sin(2x)=0

sin (6 x) + sin (2 x) = 0

cos (a) = - \frac{1}{2}

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

sin^2(θ)=2cos(θ)+2

sin^{2} (θ) = 2 cos (θ) + 2