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受欢迎的三角函数 >

cos(4t)=0

解答

cos (4 t) = 0

解答

t = \frac{π}{8} + \frac{πn}{2}, t = \frac{3 π}{8} + \frac{πn}{2}

+1

度数

t = 22. 5^{\circ} + 9 0^{\circ} n, t = 67. 5^{\circ} + 9 0^{\circ} n

求解步骤

cos (4 t) = 0

cos (4 t) = 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}

4 t = \frac{π}{2} + 2 πn, 4 t = \frac{3 π}{2} + 2 πn

4 t = \frac{π}{2} + 2 πn, 4 t = \frac{3 π}{2} + 2 πn

解

4 t = \frac{π}{2} + 2 πn : t = \frac{π}{8} + \frac{πn}{2}

4 t = \frac{π}{2} + 2 πn

两边除以

4

4 t = \frac{π}{2} + 2 πn

两边除以

4

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

化简

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

化简

\frac{4 t}{4} : t

\frac{4 t}{4}

数字相除:

\frac{4}{4} = 1

= t

化简

\frac{\frac{π}{2}}{4} + \frac{2 πn}{4} : \frac{π}{8} + \frac{πn}{2}

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

\frac{\frac{π}{2}}{4} = \frac{π}{8}

\frac{\frac{π}{2}}{4}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{π}{8}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{π}{8} + \frac{πn}{2}

t = \frac{π}{8} + \frac{πn}{2}

t = \frac{π}{8} + \frac{πn}{2}

t = \frac{π}{8} + \frac{πn}{2}

解

4 t = \frac{3 π}{2} + 2 πn : t = \frac{3 π}{8} + \frac{πn}{2}

4 t = \frac{3 π}{2} + 2 πn

两边除以

4

4 t = \frac{3 π}{2} + 2 πn

两边除以

4

\frac{4 t}{4} = \frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4}

化简

\frac{4 t}{4} = \frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4}

化简

\frac{4 t}{4} : t

\frac{4 t}{4}

数字相除:

\frac{4}{4} = 1

= t

化简

\frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4} : \frac{3 π}{8} + \frac{πn}{2}

\frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4}

\frac{\frac{3 π}{2}}{4} = \frac{3 π}{8}

\frac{\frac{3 π}{2}}{4}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{3 π}{8}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{3 π}{8} + \frac{πn}{2}

t = \frac{3 π}{8} + \frac{πn}{2}

t = \frac{3 π}{8} + \frac{πn}{2}

t = \frac{3 π}{8} + \frac{πn}{2}

t = \frac{π}{8} + \frac{πn}{2}, t = \frac{3 π}{8} + \frac{πn}{2}

作图

流行的例子

cot (\frac{1}{2} x) - 1 = 0

8cos^2(θ)-3cos(θ)=0,0<= θ<= 180

8 cos^{2} (θ) - 3 cos (θ) = 0, 0^{\circ} \leq θ \leq 18 0^{\circ}

8 sin (x) - 7 = 0

sec (t) = 2

tan(x+2)=cot(4x+28)

tan (x + 2) = cot (4 x + 28)