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受欢迎的三角函数 >

(((1-sin^2(x)))/((1+2*sin^2(x))))=0.45

解答

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 \cdot sin ^{2} ( x ) )}) = 0.45

解答

x = 0.56809 \dots + 2 πn, x = π - 0.56809 \dots + 2 πn, x = - 0.56809 \dots + 2 πn, x = π + 0.56809 \dots + 2 πn

+1

度数

x = 32.54946 \dots^{\circ} + 36 0^{\circ} n, x = 147.45053 \dots^{\circ} + 36 0^{\circ} n, x = - 32.54946 \dots^{\circ} + 36 0^{\circ} n, x = 212.54946 \dots^{\circ} + 36 0^{\circ} n

求解步骤

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 sin ^{2} ( x ) )}) = 0.45

用替代法求解

\frac{1 - sin ^{2} ( x )}{1 + 2 sin ^{2} ( x )} = 0.45

令

: sin (x) = u

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45 : u = \frac{11}{38}, u = - \frac{11}{38}

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45

在两边乘以

1 + 2 u^{2}

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45

在两边乘以

1 + 2 u^{2}

\frac{1 - u ^{2}}{1 + 2 u ^{2}} (1 + 2 u^{2}) = 0.45 (1 + 2 u^{2})

化简

1 - u^{2} = 0.45 (1 + 2 u^{2})

1 - u^{2} = 0.45 (1 + 2 u^{2})

解

1 - u^{2} = 0.45 (1 + 2 u^{2}) : u = \frac{11}{38}, u = - \frac{11}{38}

1 - u^{2} = 0.45 (1 + 2 u^{2})

展开

0.45 (1 + 2 u^{2}) : 0.45 + 0.9 u^{2}

0.45 (1 + 2 u^{2})

使用分配律:

a (b + c) = ab + a c

a = 0.45, b = 1, c = 2 u^{2}

= 0.45 \cdot 1 + 0.45 \cdot 2 u^{2}

= 1 \cdot 0.45 + 2 \cdot 0.45 u^{2}

化简

1 \cdot 0.45 + 2 \cdot 0.45 u^{2} : 0.45 + 0.9 u^{2}

1 \cdot 0.45 + 2 \cdot 0.45 u^{2}

数字相乘:

1 \cdot 0.45 = 0.45

= 0.45 + 2 \cdot 0.45 u^{2}

数字相乘:

2 \cdot 0.45 = 0.9

= 0.45 + 0.9 u^{2}

= 0.45 + 0.9 u^{2}

1 - u^{2} = 0.45 + 0.9 u^{2}

将

1

到右边

1 - u^{2} = 0.45 + 0.9 u^{2}

两边减去

1

1 - u^{2} - 1 = 0.45 + 0.9 u^{2} - 1

化简

- u^{2} = 0.9 u^{2} - 0.55

- u^{2} = 0.9 u^{2} - 0.55

将

0.9 u^{2}

para o lado esquerdo

- u^{2} = 0.9 u^{2} - 0.55

两边减去

0.9 u^{2}

- u^{2} - 0.9 u^{2} = 0.9 u^{2} - 0.55 - 0.9 u^{2}

化简

- 1.9 u^{2} = - 0.55

- 1.9 u^{2} = - 0.55

在两边乘以

100

- 1.9 u^{2} = - 0.55

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- 1.9 u^{2} \cdot 100 = - 0.55 \cdot 100

整理后得

- 190 u^{2} = - 55

- 190 u^{2} = - 55

两边除以

- 190

- 190 u^{2} = - 55

两边除以

- 190

\frac{- 190 u ^{2}}{- 190} = \frac{- 55}{- 190}

化简

\frac{- 190 u ^{2}}{- 190} = \frac{- 55}{- 190}

化简

\frac{- 190 u ^{2}}{- 190} : u^{2}

\frac{- 190 u ^{2}}{- 190}

使用分式法则:

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

= \frac{190 u ^{2}}{190}

数字相除:

\frac{190}{190} = 1

= u^{2}

化简

\frac{- 55}{- 190} : \frac{11}{38}

\frac{- 55}{- 190}

使用分式法则:

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

= \frac{55}{190}

约分:

5

= \frac{11}{38}

u^{2} = \frac{11}{38}

u^{2} = \frac{11}{38}

u^{2} = \frac{11}{38}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{11}{38}, u = - \frac{11}{38}

u = \frac{11}{38}, u = - \frac{11}{38}

u = sin (x)

代回

sin (x) = \frac{11}{38}, sin (x) = - \frac{11}{38}

sin (x) = \frac{11}{38}, sin (x) = - \frac{11}{38}

sin (x) = \frac{11}{38} : x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn

sin (x) = \frac{11}{38}

使用反三角函数性质

sin (x) = \frac{11}{38}

sin (x) = \frac{11}{38}

的通解

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

x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn

x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn

sin (x) = - \frac{11}{38} : x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

sin (x) = - \frac{11}{38}

使用反三角函数性质

sin (x) = - \frac{11}{38}

sin (x) = - \frac{11}{38}

的通解

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

x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

合并所有解

x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn, x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

以小数形式表示解

x = 0.56809 \dots + 2 πn, x = π - 0.56809 \dots + 2 πn, x = - 0.56809 \dots + 2 πn, x = π + 0.56809 \dots + 2 πn

作图

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