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受欢迎的三角函数 >

8cos(a)-15sin(a)=0

解答

8 cos (a) - 15 sin (a) = 0

解答

a = 0.48995 \dots + πn

+1

度数

a = 28.07248 \dots^{\circ} + 18 0^{\circ} n

求解步骤

8 cos (a) - 15 sin (a) = 0

使用三角恒等式改写

8 cos (a) - 15 sin (a) = 0

在两边除以

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

\frac{8 cos ( a ) - 15 sin ( a )}{cos ( a )} = \frac{0}{cos ( a )}

化简

8 - \frac{15 sin ( a )}{cos ( a )} = 0

使用基本三角恒等式:

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

8 - 15 tan (a) = 0

8 - 15 tan (a) = 0

将

8

到右边

8 - 15 tan (a) = 0

两边减去

8

8 - 15 tan (a) - 8 = 0 - 8

化简

- 15 tan (a) = - 8

- 15 tan (a) = - 8

两边除以

- 15

- 15 tan (a) = - 8

两边除以

- 15

\frac{- 15 tan ( a )}{- 15} = \frac{- 8}{- 15}

化简

tan (a) = \frac{8}{15}

tan (a) = \frac{8}{15}

使用反三角函数性质

tan (a) = \frac{8}{15}

tan (a) = \frac{8}{15}

的通解

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

a = arctan (\frac{8}{15}) + πn

a = arctan (\frac{8}{15}) + πn

以小数形式表示解

a = 0.48995 \dots + πn

作图

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