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受欢迎的三角函数 >

(cos^{2022}(x))/((sin^{2022)(x)+cos^{2022}(x))}=1

解答

\frac{cos ^{2022} ( x )}{( sin ^{2022} ( x ) + cos ^{2022} ( x ) )} = 1

解答

x = 2 πn, x = π + 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

\frac{cos ^{2022} ( x )}{( sin ^{2022} ( x ) + cos ^{2022} ( x ) )} = 1

两边减去

1

\frac{cos ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} - 1 = 0

化简

\frac{cos ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} - 1 : - \frac{sin ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )}

\frac{cos ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} - 1

将项转换为分式:

1 = \frac{1 ( sin ^{2022} ( x ) + cos ^{2022} ( x ) )}{sin ^{2022} ( x ) + cos ^{2022} ( x )}

= \frac{cos ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} - \frac{1 \cdot ( sin ^{2022} ( x ) + cos ^{2022} ( x ) )}{sin ^{2022} ( x ) + cos ^{2022} ( 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 ^{2022} ( x ) - 1 \cdot ( sin ^{2022} ( x ) + cos ^{2022} ( x ) )}{sin ^{2022} ( x ) + cos ^{2022} ( x )}

乘以:

1 \cdot (sin^{2022} (x) + cos^{2022} (x)) = (sin^{2022} (x) + cos^{2022} (x))

= \frac{cos ^{2022} ( x ) - ( sin ^{2022} ( x ) + cos ^{2022} ( x ) )}{sin ^{2022} ( x ) + cos ^{2022} ( x )}

乘开

cos^{2022} (x) - (sin^{2022} (x) + cos^{2022} (x)) : - sin^{2022} (x)

cos^{2022} (x) - (sin^{2022} (x) + cos^{2022} (x))

- (sin^{2022} (x) + cos^{2022} (x)) : - sin^{2022} (x) - cos^{2022} (x)

- (sin^{2022} (x) + cos^{2022} (x))

打开括号

= - (sin^{2022} (x)) - (cos^{2022} (x))

使用加减运算法则

+ (- a) = - a

= - sin^{2022} (x) - cos^{2022} (x)

= cos^{2022} (x) - sin^{2022} (x) - cos^{2022} (x)

同类项相加:

cos^{2022} (x) - cos^{2022} (x) = 0

= - sin^{2022} (x)

= \frac{- sin ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{sin ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )}

- \frac{sin ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} = 0

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

- (sin^{2022} (x)) = 0

两边除以

- 1

- (sin^{2022} (x)) = 0

两边除以

- 1

\frac{- sin ^{2022} ( x )}{- 1} = \frac{0}{- 1}

化简

sin^{2022} (x) = 0

sin^{2022} (x) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

sin (x) = 0

解是

sin (x) = 0

sin (x) = 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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

作图

流行的例子

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sin^{3} (x) = - 1

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