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受欢迎的三角函数 >

((320/3))/((sin(30)+cos(30)))

解答

\frac{( \frac{320}{3} )}{( sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} ) )}

解答

- \frac{320 ( 1 - 3 )}{3}

+1

十进制

78.08541 \dots

求解步骤

\frac{( \frac{320}{3} )}{( sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} ) )}

= \frac{\frac{320}{3}}{sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\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{1}{2}

使用以下普通恒等式:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\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{3}{2}

= \frac{\frac{320}{3}}{\frac{1}{2} + \frac{3}{2}}

化简

\frac{\frac{320}{3}}{\frac{1}{2} + \frac{3}{2}} : - \frac{320 ( 1 - 3 )}{3}

\frac{\frac{320}{3}}{\frac{1}{2} + \frac{3}{2}}

合并分式

\frac{1}{2} + \frac{3}{2} : \frac{1 + 3}{2}

使用法则

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

= \frac{1 + 3}{2}

= \frac{\frac{320}{3}}{\frac{1 + 3}{2}}

分式相除:

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

= \frac{320 \cdot 2}{3 ( 1 + 3 )}

数字相乘:

320 \cdot 2 = 640

= \frac{640}{3 ( 1 + 3 )}

\frac{640}{3 ( 1 + 3 )}

有理化:

- \frac{320 ( 1 - 3 )}{3}

\frac{640}{3 ( 1 + 3 )}

乘以共轭根式

\frac{1 - 3}{1 - 3}

= \frac{640 ( 1 - 3 )}{3 ( 1 + 3 ) ( 1 - 3 )}

3 (1 + 3) (1 - 3) = - 6

3 (1 + 3) (1 - 3)

乘开

(1 + 3) (1 - 3) : - 2

(1 + 3) (1 - 3)

使用平方差公式:

(a + b) (a - b) = a^{2} - b^{2}

a = 1, b = 3

= 1^{2} - (3)^{2}

化简

1^{2} - (3)^{2} : - 2

1^{2} - (3)^{2}

使用法则

1^{a} = 1

1^{2} = 1

= 1 - (3)^{2}

(3)^{2} = 3

(3)^{2}

使用根式运算法则:

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

= (3^{\frac{1}{2}})^{2}

使用指数法则:

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

= 3^{\frac{1}{2} \cdot 2}

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

\frac{1}{2} \cdot 2

分式相乘:

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

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

约分:

2

= 1

= 3

= 1 - 3

数字相减:

1 - 3 = - 2

= - 2

= - 2

= 3 (- 2)

乘开

3 (- 2) : - 6

3 (- 2)

打开括号

= 3 (- 2)

使用加减运算法则

+ (- a) = - a

= - 3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= - 6

= - 6

= \frac{640 ( 1 - 3 )}{- 6}

使用分式法则:

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

= - \frac{640 ( 1 - 3 )}{6}

约分:

2

= - \frac{320 ( 1 - 3 )}{3}

= - \frac{320 ( 1 - 3 )}{3}

= - \frac{320 ( 1 - 3 )}{3}

流行的例子

sin(60)-tan(45)

sin (6 0^{\circ}) - tan (4 5^{\circ})

(4 cos (3 0^{\circ}))^{2}

(tan(0))/(sec(0))

\frac{tan ( 0 )}{sec ( 0 )}

tan (37. 5^{\circ})

\frac{2}{cos ( 2 0 ^{\circ} )}