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受欢迎的三角函数 >

(sin(pi/3)tan(pi/6)+csc(pi/4))^2

解答

(sin (\frac{π}{3}) tan (\frac{π}{6}) + csc (\frac{π}{4}))^{2}

解答

2 + \frac{9}{4}

+1

十进制

3.66421 \dots

求解步骤

(sin (\frac{π}{3}) tan (\frac{π}{6}) + csc (\frac{π}{4}))^{2}

使用以下普通恒等式:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

使用以下普通恒等式:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

tan (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

使用以下普通恒等式:

csc (\frac{π}{4}) = 2

csc (\frac{π}{4})

csc (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= (\frac{3}{2} \cdot \frac{3}{3} + 2)^{2}

化简

(\frac{3}{2} \cdot \frac{3}{3} + 2)^{2} : 2 + \frac{9}{4}

(\frac{3}{2} \cdot \frac{3}{3} + 2)^{2}

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

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

分式相乘:

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

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

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

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

数字相乘:

2 \cdot 3 = 6

= \frac{3}{6}

约分:

3

= \frac{1}{2}

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

使用完全平方公式:

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

a = \frac{1}{2}, b = 2

= (\frac{1}{2})^{2} + 2 \cdot \frac{1}{2} 2 + (2)^{2}

化简

(\frac{1}{2})^{2} + 2 \cdot \frac{1}{2} 2 + (2)^{2} : 2 + \frac{9}{4}

(\frac{1}{2})^{2} + 2 \cdot \frac{1}{2} 2 + (2)^{2}

(\frac{1}{2})^{2} = \frac{1}{4}

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

使用指数法则:

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

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

使用法则

1^{a} = 1

1^{2} = 1

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

2^{2} = 4

= \frac{1}{4}

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

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

分式相乘:

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

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

约分:

2

= 1 \cdot 2

乘以:

1 \cdot 2 = 2

= 2

(2)^{2} = 2

(2)^{2}

使用根式运算法则:

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

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

使用指数法则:

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

= 2^{\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

= 2

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

合并分式

2 + \frac{1}{4} : \frac{9}{4}

2 + \frac{1}{4}

将项转换为分式:

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

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

因为分母相等，所以合并分式:

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

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

2 \cdot 4 + 1 = 9

2 \cdot 4 + 1

数字相乘:

2 \cdot 4 = 8

= 8 + 1

数字相加:

8 + 1 = 9

= 9

= \frac{9}{4}

= 2 + \frac{9}{4}

= 2 + \frac{9}{4}

= 2 + \frac{9}{4}

流行的例子

sinh (2 ln (5))

10 sin (27 0^{\circ})

sin (1) - 1

cos (2 (π))

arccos(cos((7pi)/5))

arccos (cos (\frac{7 π}{5}))