zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

15sin^2(x)-17sin(x)+4=0

解答

15 sin^{2} (x) - 17 sin (x) + 4 = 0

解答

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn, x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

+1

度数

x = 53.13010 \dots^{\circ} + 36 0^{\circ} n, x = 126.86989 \dots^{\circ} + 36 0^{\circ} n, x = 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 160.52877 \dots^{\circ} + 36 0^{\circ} n

求解步骤

15 sin^{2} (x) - 17 sin (x) + 4 = 0

用替代法求解

15 sin^{2} (x) - 17 sin (x) + 4 = 0

令

: sin (x) = u

15 u^{2} - 17 u + 4 = 0

15 u^{2} - 17 u + 4 = 0 : u = \frac{4}{5}, u = \frac{1}{3}

15 u^{2} - 17 u + 4 = 0

使用求根公式求解

15 u^{2} - 17 u + 4 = 0

二次方程求根公式:

若

a = 15, b = - 17, c = 4

u_{1, 2} = \frac{- ( - 17 ) \pm ( - 17 ) ^{2} - 4 \cdot 15 \cdot 4}{2 \cdot 15}

u_{1, 2} = \frac{- ( - 17 ) \pm ( - 17 ) ^{2} - 4 \cdot 15 \cdot 4}{2 \cdot 15}

(- 17)^{2} - 4 \cdot 15 \cdot 4 = 7

(- 17)^{2} - 4 \cdot 15 \cdot 4

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 17)^{2} = 1 7^{2}

= 1 7^{2} - 4 \cdot 15 \cdot 4

数字相乘:

4 \cdot 15 \cdot 4 = 240

= 1 7^{2} - 240

1 7^{2} = 289

= 289 - 240

数字相减:

289 - 240 = 49

= 49

因式分解数字:

49 = 7^{2}

= 7^{2}

使用根式运算法则:

n a^{n} = a

7^{2} = 7

= 7

u_{1, 2} = \frac{- ( - 17 ) \pm 7}{2 \cdot 15}

将解分隔开

u_{1} = \frac{- ( - 17 ) + 7}{2 \cdot 15}, u_{2} = \frac{- ( - 17 ) - 7}{2 \cdot 15}

u = \frac{- ( - 17 ) + 7}{2 \cdot 15} : \frac{4}{5}

\frac{- ( - 17 ) + 7}{2 \cdot 15}

使用法则

- (- a) = a

= \frac{17 + 7}{2 \cdot 15}

数字相加:

17 + 7 = 24

= \frac{24}{2 \cdot 15}

数字相乘:

2 \cdot 15 = 30

= \frac{24}{30}

约分:

6

= \frac{4}{5}

u = \frac{- ( - 17 ) - 7}{2 \cdot 15} : \frac{1}{3}

\frac{- ( - 17 ) - 7}{2 \cdot 15}

使用法则

- (- a) = a

= \frac{17 - 7}{2 \cdot 15}

数字相减:

17 - 7 = 10

= \frac{10}{2 \cdot 15}

数字相乘:

2 \cdot 15 = 30

= \frac{10}{30}

约分:

10

= \frac{1}{3}

二次方程组的解是:

u = \frac{4}{5}, u = \frac{1}{3}

u = sin (x)

代回

sin (x) = \frac{4}{5}, sin (x) = \frac{1}{3}

sin (x) = \frac{4}{5}, sin (x) = \frac{1}{3}

sin (x) = \frac{4}{5} : x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

sin (x) = \frac{4}{5}

使用反三角函数性质

sin (x) = \frac{4}{5}

sin (x) = \frac{4}{5}

的通解

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

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

sin (x) = \frac{1}{3} : x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

sin (x) = \frac{1}{3}

使用反三角函数性质

sin (x) = \frac{1}{3}

sin (x) = \frac{1}{3}

的通解

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

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

合并所有解

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn, x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

以小数形式表示解

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn, x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

作图

流行的例子

tan^2(x)=2sec(x)

tan^{2} (x) = 2 sec (x)

-sin^2(x)=sin^4(x)

- sin^{2} (x) = sin^{4} (x)

3cos^2(x)=sin(2x)*sin(x)

3 cos^{2} (x) = sin (2 x) \cdot sin (x)

csc (t) = 2

arccosh(θ)=0.86806

arccosh (θ) = 0.86806