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受欢迎的三角函数 >

cos(x)=(cos(x))/(csc(x))

解答

cos (x) = \frac{cos ( x )}{csc ( x )}

解答

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

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) = \frac{cos ( x )}{csc ( x )}

两边减去

\frac{cos ( x )}{csc ( x )}

cos (x) - \frac{cos ( x )}{csc ( x )} = 0

化简

cos (x) - \frac{cos ( x )}{csc ( x )} : \frac{cos ( x ) csc ( x ) - cos ( x )}{csc ( x )}

cos (x) - \frac{cos ( x )}{csc ( x )}

将项转换为分式:

cos (x) = \frac{cos ( x ) csc ( x )}{csc ( x )}

= \frac{cos ( x ) csc ( x )}{csc ( x )} - \frac{cos ( x )}{csc ( x )}

因为分母相等，所以合并分式:

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

= \frac{cos ( x ) csc ( x ) - cos ( x )}{csc ( x )}

\frac{cos ( x ) csc ( x ) - cos ( x )}{csc ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos (x) csc (x) - cos (x) = 0

分解

cos (x) csc (x) - cos (x) : cos (x) (csc (x) - 1)

cos (x) csc (x) - cos (x)

因式分解出通项

cos (x)

= cos (x) (csc (x) - 1)

cos (x) (csc (x) - 1) = 0

分别求解每个部分

cos (x) = 0 or csc (x) - 1 = 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

csc (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

csc (x) - 1 = 0

将

1

到右边

csc (x) - 1 = 0

两边加上

1

csc (x) - 1 + 1 = 0 + 1

化简

csc (x) = 1

csc (x) = 1

csc (x) = 1

的通解

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

合并所有解

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

作图

流行的例子

cos(θ)= 1/(sqrt(1^2+(4)^2+8^2))

cos (θ) = \frac{1}{1 ^{2} + ( 4 ) ^{2} + 8 ^{2}}

2+3cot^2(x)-3csc(x)=5

2 + 3 cot^{2} (x) - 3 csc (x) = 5

- 2 = - 2 + tan (θ)

cos (A) = 0.65

sin(3x-pi/4)=(sqrt(2))/2

sin (3 x - \frac{π}{4}) = \frac{2}{2}