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受欢迎的三角函数 >

sin(t)=(250)/(sqrt(250^2+300^2))

解答

sin (t) = \frac{250}{25 0 ^{2} + 30 0 ^{2}}

解答

t = 0.69473 \dots + 2 πn, t = π - 0.69473 \dots + 2 πn

+1

弧度

t = 0.69473 \dots + 6.28318 \dots n, t = π - 0.69473 \dots + 6.28318 \dots n

求解步骤

sin (t) = \frac{250}{25 0 ^{2} + 30 0 ^{2}}

化简

\frac{250}{25 0 ^{2} + 30 0 ^{2}} : \frac{5 61}{61}

\frac{250}{25 0 ^{2} + 30 0 ^{2}}

25 0^{2} + 30 0^{2} = 152500

25 0^{2} + 30 0^{2}

25 0^{2} = 62500

= 62500 + 30 0^{2}

30 0^{2} = 90000

= 62500 + 90000

数字相加:

62500 + 90000 = 152500

= 152500

= \frac{250}{152500}

分解

250 : 5^{3} \cdot 2

因式分解

250 = 5^{3} \cdot 2

分解

152500 : 5^{2} \cdot 261

因式分解

152500 = 5^{4} \cdot 2^{2} \cdot 61

= 5^{4} \cdot 2^{2} \cdot 61

使用根式运算法则:

n ab = n a n b

= 61 2^{2} 5^{4}

化简

2^{2} : 2

2^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 2

化简

5^{4} : 5^{2}

5^{4}

使用指数法则:

a^{b c} = (a^{b})^{c}

5^{4} = 5^{2 \cdot 2} = (5^{2})^{2}

= (5^{2})^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 5^{2}

= 5^{2} \cdot 261

= \frac{5 ^{3} \cdot 2}{5 ^{2} \cdot 2 61}

消掉

\frac{2 \cdot 5 ^{3}}{2 \cdot 5 ^{2} 61} : \frac{5}{61}

\frac{2 \cdot 5 ^{3}}{2 \cdot 5 ^{2} 61}

数字相除:

\frac{2}{2} = 1

= \frac{5 ^{3}}{5 ^{2} 61}

使用指数法则:

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

\frac{5 ^{3}}{5 ^{2}} = 5^{3 - 2}

= \frac{5 ^{3 - 2}}{61}

数字相减:

3 - 2 = 1

= \frac{5}{61}

= \frac{5}{61}

\frac{5}{61}

有理化:

\frac{5 61}{61}

\frac{5}{61}

乘以共轭根式

\frac{61}{61}

= \frac{5 61}{61 61}

6161 = 61

6161

使用根式运算法则:

a a = a

6161 = 61

= 61

= \frac{5 61}{61}

= \frac{5 61}{61}

sin (t) = \frac{5 61}{61}

使用反三角函数性质

sin (t) = \frac{5 61}{61}

sin (t) = \frac{5 61}{61}

的通解

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

t = arcsin (\frac{5 61}{61}) + 2 πn, t = π - arcsin (\frac{5 61}{61}) + 2 πn

t = arcsin (\frac{5 61}{61}) + 2 πn, t = π - arcsin (\frac{5 61}{61}) + 2 πn

以小数形式表示解

t = 0.69473 \dots + 2 πn, t = π - 0.69473 \dots + 2 πn

作图

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