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受欢迎的三角函数 >

(sin(60)+1)^2

解答

(sin (6 0^{\circ}) + 1)^{2}

解答

3 + \frac{7}{4}

+1

十进制

3.48205 \dots

求解步骤

(sin (6 0^{\circ}) + 1)^{2}

使用以下普通恒等式:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

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

化简

(\frac{3}{2} + 1)^{2} : 3 + \frac{7}{4}

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

使用完全平方公式:

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

a = \frac{3}{2}, b = 1

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

化简

(\frac{3}{2})^{2} + 2 \cdot \frac{3}{2} \cdot 1 + 1^{2} : 3 + \frac{7}{4}

(\frac{3}{2})^{2} + 2 \cdot \frac{3}{2} \cdot 1 + 1^{2}

使用法则

1^{a} = 1

1^{2} = 1

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

(\frac{3}{2})^{2} = \frac{3}{4}

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

使用指数法则:

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

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

(3)^{2} : 3

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

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

2^{2} = 4

= \frac{3}{4}

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

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

分式相乘:

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

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

约分:

2

= 1 \cdot 3

乘以:

1 \cdot 3 = 3

= 3

= \frac{3}{4} + 3 + 1

合并分式

1 + \frac{3}{4} : \frac{7}{4}

1 + \frac{3}{4}

将项转换为分式:

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

= \frac{1 \cdot 4}{4} + \frac{3}{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{1 \cdot 4 + 3}{4}

1 \cdot 4 + 3 = 7

1 \cdot 4 + 3

数字相乘:

1 \cdot 4 = 4

= 4 + 3

数字相加:

4 + 3 = 7

= 7

= \frac{7}{4}

= 3 + \frac{7}{4}

= 3 + \frac{7}{4}

= 3 + \frac{7}{4}

流行的例子

cos^2(10)-sin^2(10)

cos^{2} (1 0^{\circ}) - sin^{2} (1 0^{\circ})

3cos(pi/2)sin(pi/2)

3 cos (\frac{π}{2}) sin (\frac{π}{2})

1.33 sin (4 5^{\circ})

cos (- 3 5^{\circ})

arctan(-1)-arctan(0.5)(-1)

arctan (- 1) - arctan (0.5) (- 1)