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受欢迎的三角函数 >

cos(8t)-5sin(8t)=0

解答

cos (8 t) - 5 sin (8 t) = 0

解答

t = \frac{0.19739 \dots}{8} + \frac{πn}{8}

+1

度数

t = 1.41374 \dots^{\circ} + 22. 5^{\circ} n

求解步骤

cos (8 t) - 5 sin (8 t) = 0

使用三角恒等式改写

cos (8 t) - 5 sin (8 t) = 0

在两边除以

cos (8 t), cos (8 t) \neq = 0

\frac{cos ( 8 t ) - 5 sin ( 8 t )}{cos ( 8 t )} = \frac{0}{cos ( 8 t )}

化简

1 - \frac{5 sin ( 8 t )}{cos ( 8 t )} = 0

使用基本三角恒等式:

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

1 - 5 tan (8 t) = 0

1 - 5 tan (8 t) = 0

将

1

到右边

1 - 5 tan (8 t) = 0

两边减去

1

1 - 5 tan (8 t) - 1 = 0 - 1

化简

- 5 tan (8 t) = - 1

- 5 tan (8 t) = - 1

两边除以

- 5

- 5 tan (8 t) = - 1

两边除以

- 5

\frac{- 5 tan ( 8 t )}{- 5} = \frac{- 1}{- 5}

化简

tan (8 t) = \frac{1}{5}

tan (8 t) = \frac{1}{5}

使用反三角函数性质

tan (8 t) = \frac{1}{5}

tan (8 t) = \frac{1}{5}

的通解

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

8 t = arctan (\frac{1}{5}) + πn

8 t = arctan (\frac{1}{5}) + πn

解

8 t = arctan (\frac{1}{5}) + πn : t = \frac{arctan ( \frac{1}{5} )}{8} + \frac{πn}{8}

8 t = arctan (\frac{1}{5}) + πn

两边除以

8

8 t = arctan (\frac{1}{5}) + πn

两边除以

8

\frac{8 t}{8} = \frac{arctan ( \frac{1}{5} )}{8} + \frac{πn}{8}

化简

t = \frac{arctan ( \frac{1}{5} )}{8} + \frac{πn}{8}

t = \frac{arctan ( \frac{1}{5} )}{8} + \frac{πn}{8}

t = \frac{arctan ( \frac{1}{5} )}{8} + \frac{πn}{8}

以小数形式表示解

t = \frac{0.19739 \dots}{8} + \frac{πn}{8}

作图

流行的例子

cos^2(x)+3sin(x)+1=0

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