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受欢迎的三角函数 >

9sin(x)cos(x)=-8cos(x)

解答

9 sin (x) cos (x) = - 8 cos (x)

解答

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = - 1.09491 \dots + 2 πn, x = π + 1.09491 \dots + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = - 62.73395 \dots^{\circ} + 36 0^{\circ} n, x = 242.73395 \dots^{\circ} + 36 0^{\circ} n

求解步骤

9 sin (x) cos (x) = - 8 cos (x)

两边减去

- 8 cos (x)

9 sin (x) cos (x) + 8 cos (x) = 0

分解

9 sin (x) cos (x) + 8 cos (x) : cos (x) (9 sin (x) + 8)

9 sin (x) cos (x) + 8 cos (x)

因式分解出通项

cos (x)

= cos (x) (9 sin (x) + 8)

cos (x) (9 sin (x) + 8) = 0

分别求解每个部分

cos (x) = 0 or 9 sin (x) + 8 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

cos (x) = 0

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

9 sin (x) + 8 = 0 : x = arcsin (- \frac{8}{9}) + 2 πn, x = π + arcsin (\frac{8}{9}) + 2 πn

9 sin (x) + 8 = 0

将

8

到右边

9 sin (x) + 8 = 0

两边减去

8

9 sin (x) + 8 - 8 = 0 - 8

化简

9 sin (x) = - 8

9 sin (x) = - 8

两边除以

9

9 sin (x) = - 8

两边除以

9

\frac{9 sin ( x )}{9} = \frac{- 8}{9}

化简

sin (x) = - \frac{8}{9}

sin (x) = - \frac{8}{9}

使用反三角函数性质

sin (x) = - \frac{8}{9}

sin (x) = - \frac{8}{9}

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{8}{9}) + 2 πn, x = π + arcsin (\frac{8}{9}) + 2 πn

x = arcsin (- \frac{8}{9}) + 2 πn, x = π + arcsin (\frac{8}{9}) + 2 πn

合并所有解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arcsin (- \frac{8}{9}) + 2 πn, x = π + arcsin (\frac{8}{9}) + 2 πn

以小数形式表示解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = - 1.09491 \dots + 2 πn, x = π + 1.09491 \dots + 2 πn

作图

流行的例子

8 sin (8 x) + 9 = 3

4 sin (θ) + 2 = 0

cot(x)(tan(x)+1)=0

cot (x) (tan (x) + 1) = 0

4 sin (θ) + 3 = 5

5sin(x)cos(x)=7cos(x)

5 sin (x) cos (x) = 7 cos (x)