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受欢迎的三角函数 >

(706.32)/(sin(45)1.5+cos(45)0.5)

解答

\frac{706.32}{sin ( 4 5 ^{\circ} ) 1.5 + cos ( 4 5 ^{\circ} ) 0.5}

解答

\frac{8829 2}{25}

+1

十进制

499.44366 \dots

求解步骤

\frac{706.32}{sin ( 4 5 ^{\circ} ) \cdot 1.5 + cos ( 4 5 ^{\circ} ) \cdot 0.5}

= \frac{\frac{17658}{25}}{sin ( 4 5 ^{\circ} ) \frac{3}{2} + cos ( 4 5 ^{\circ} ) \frac{1}{2}}

使用以下普通恒等式:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

使用以下普通恒等式:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{\frac{17658}{25}}{\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}}

化简

\frac{\frac{17658}{25}}{\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}} : \frac{8829 2}{25}

\frac{\frac{17658}{25}}{\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}}

使用分式法则:

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

= \frac{17658}{25 ( \frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} )}

\frac{2}{2} \cdot \frac{3}{2} = \frac{3 2}{4}

\frac{2}{2} \cdot \frac{3}{2}

分式相乘:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 \cdot 3}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{3 2}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

\frac{2}{2} \cdot \frac{1}{2}

分式相乘:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 \cdot 1}{2 \cdot 2}

乘以:

2 \cdot 1 = 2

= \frac{2}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{17658}{25 ( \frac{2}{4} + \frac{3 2}{4} )}

合并分式

\frac{3 2}{4} + \frac{2}{4} : 2

使用法则

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

= \frac{3 2 + 2}{4}

同类项相加:

32 + 2 = 42

= \frac{4 2}{4}

数字相除:

\frac{4}{4} = 1

= 2

= \frac{17658}{25 ( 2 )}

去除括号:

(a) = a

= \frac{17658}{25 2}

分解

17658 : 3^{4} \cdot 2 \cdot 109

因式分解

17658 = 3^{4} \cdot 2 \cdot 109

= \frac{3 ^{4} \cdot 2 \cdot 109}{25 2}

消掉

\frac{2 \cdot 3 ^{4} \cdot 109}{25 2} : \frac{2 \cdot 3 ^{4} \cdot 109}{25}

\frac{2 \cdot 3 ^{4} \cdot 109}{25 2}

使用根式运算法则:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{3 ^{4} \cdot 2 \cdot 109}{25 \cdot 2 ^{\frac{1}{2}}}

使用指数法则:

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

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= \frac{3 ^{4} \cdot 109 \cdot 2 ^{- \frac{1}{2} + 1}}{25}

数字相减:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{3 ^{4} \cdot 109 \cdot 2 ^{\frac{1}{2}}}{25}

使用根式运算法则:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= \frac{3 ^{4} \cdot 109 2}{25}

= \frac{2 \cdot 3 ^{4} \cdot 109}{25}

2 \cdot 3^{4} \cdot 109 = 88292

2 \cdot 3^{4} \cdot 109

3^{4} = 81

= 81 \cdot 1092

数字相乘:

81 \cdot 109 = 8829

= 88292

= \frac{8829 2}{25}

= \frac{8829 2}{25}

流行的例子

2(cos^2(15)-sin^2(15))

2 (cos^{2} (1 5^{\circ}) - sin^{2} (1 5^{\circ}))

- 4 sin (\frac{3 π}{4})

tan(-(13pi)/(12))

tan (- \frac{13 π}{12})

cosh (9)

tanh (2)