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受欢迎的三角函数 >

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

解答

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

解答

x = 0.46364 \dots + πn

+1

度数

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

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

交换两边

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

使用三角恒等式改写

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

在两边除以

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

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

化简

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

使用基本三角恒等式:

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

- 2 tan (x) + 1 = 0

- 2 tan (x) + 1 = 0

将

1

到右边

- 2 tan (x) + 1 = 0

两边减去

1

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

化简

- 2 tan (x) = - 1

- 2 tan (x) = - 1

两边除以

- 2

- 2 tan (x) = - 1

两边除以

- 2

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

化简

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

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

使用反三角函数性质

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

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

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{1}{2}) + πn

x = arctan (\frac{1}{2}) + πn

以小数形式表示解

x = 0.46364 \dots + πn

作图

流行的例子

tan (θ) = \frac{7}{6}

2 sin (x) + 5 = 6

sin(2θ)-cos(2θ)=1

sin (2 θ) - cos (2 θ) = 1

cos(θ)= 1/(sqrt(3))

cos (θ) = \frac{1}{3}

tan(x)+1/(tan(x))=2

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