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受欢迎的三角函数 >

7.5sin(x)=3.4cos(x)

解答

7.5 sin (x) = 3.4 cos (x)

解答

x = 0.42562 \dots + πn

+1

度数

x = 24.38637 \dots^{\circ} + 18 0^{\circ} n

求解步骤

7.5 sin (x) = 3.4 cos (x)

使用三角恒等式改写

7.5 sin (x) = 3.4 cos (x)

在两边除以

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

\frac{7.5 sin ( x )}{cos ( x )} = \frac{3.4 cos ( x )}{cos ( x )}

化简

\frac{7.5 sin ( x )}{cos ( x )} = 3.4

使用基本三角恒等式:

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

7.5 tan (x) = 3.4

7.5 tan (x) = 3.4

在两边乘以

10

7.5 tan (x) = 3.4

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

7.5 tan (x) \cdot 10 = 3.4 \cdot 10

整理后得

75 tan (x) = 34

75 tan (x) = 34

两边除以

75

75 tan (x) = 34

两边除以

75

\frac{75 tan ( x )}{75} = \frac{34}{75}

化简

tan (x) = \frac{34}{75}

tan (x) = \frac{34}{75}

使用反三角函数性质

tan (x) = \frac{34}{75}

tan (x) = \frac{34}{75}

的通解

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

x = arctan (\frac{34}{75}) + πn

x = arctan (\frac{34}{75}) + πn

以小数形式表示解

x = 0.42562 \dots + πn

作图

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