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受欢迎的三角函数 >

2sin(4t)=2sin(4t)cos(4t)

解答

2 sin (4 t) = 2 sin (4 t) cos (4 t)

解答

t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

+1

度数

t = 0^{\circ} + 9 0^{\circ} n, t = 4 5^{\circ} + 9 0^{\circ} n

求解步骤

2 sin (4 t) = 2 sin (4 t) cos (4 t)

两边减去

2 sin (4 t) cos (4 t)

2 sin (4 t) - 2 sin (4 t) cos (4 t) = 0

分解

2 sin (4 t) - 2 sin (4 t) cos (4 t) : - 2 sin (4 t) (cos (4 t) - 1)

2 sin (4 t) - 2 sin (4 t) cos (4 t)

因式分解出通项

- 2 sin (4 t)

= - 2 sin (4 t) (- 1 + cos (4 t))

- 2 sin (4 t) (cos (4 t) - 1) = 0

分别求解每个部分

sin (4 t) = 0 or cos (4 t) - 1 = 0

sin (4 t) = 0 : t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

sin (4 t) = 0

sin (4 t) = 0

的通解

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

4 t = 0 + 2 πn, 4 t = π + 2 πn

4 t = 0 + 2 πn, 4 t = π + 2 πn

解

4 t = 0 + 2 πn : t = \frac{πn}{2}

4 t = 0 + 2 πn

0 + 2 πn = 2 πn

4 t = 2 πn

两边除以

4

4 t = 2 πn

两边除以

4

\frac{4 t}{4} = \frac{2 πn}{4}

化简

t = \frac{πn}{2}

t = \frac{πn}{2}

解

4 t = π + 2 πn : t = \frac{π}{4} + \frac{πn}{2}

4 t = π + 2 πn

两边除以

4

4 t = π + 2 πn

两边除以

4

\frac{4 t}{4} = \frac{π}{4} + \frac{2 πn}{4}

化简

t = \frac{π}{4} + \frac{πn}{2}

t = \frac{π}{4} + \frac{πn}{2}

t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

cos (4 t) - 1 = 0 : t = \frac{πn}{2}

cos (4 t) - 1 = 0

将

1

到右边

cos (4 t) - 1 = 0

两边加上

1

cos (4 t) - 1 + 1 = 0 + 1

化简

cos (4 t) = 1

cos (4 t) = 1

cos (4 t) = 1

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}

4 t = 0 + 2 πn

4 t = 0 + 2 πn

解

4 t = 0 + 2 πn : t = \frac{πn}{2}

4 t = 0 + 2 πn

0 + 2 πn = 2 πn

4 t = 2 πn

两边除以

4

4 t = 2 πn

两边除以

4

\frac{4 t}{4} = \frac{2 πn}{4}

化简

t = \frac{πn}{2}

t = \frac{πn}{2}

t = \frac{πn}{2}

合并所有解

t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

作图

流行的例子

a^1sin(x)=43.1253

a^{1} sin (x) = 43.1253

52800=((1500)^2sin(x))/(32.2)

52800 = \frac{( 1500 ) ^{2} sin ( x )}{32.2}

7cos(3x)=2,0<= x<2pi

7 cos (3 x) = 2, 0 \leq x < 2 π

6 cos (2 x) = 3

arctan(x/(42))=57

arctan (\frac{x}{42}) = 57