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受欢迎的三角函数 >

3sin(45)+4cos(45)

解答

3 sin (4 5^{\circ}) + 4 cos (4 5^{\circ})

解答

\frac{7 2}{2}

+1

十进制

4.94974 \dots

求解步骤

3 sin (4 5^{\circ}) + 4 cos (4 5^{\circ})

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}

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

化简

3 \cdot \frac{2}{2} + 4 \cdot \frac{2}{2} : \frac{7 2}{2}

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

同类项相加:

3 \cdot \frac{2}{2} + 4 \cdot \frac{2}{2} = 7 \cdot \frac{2}{2}

= 7 \cdot \frac{2}{2}

分式相乘:

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

= \frac{2 \cdot 7}{2}

使用根式运算法则:

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

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

= \frac{7 \cdot 2 ^{\frac{1}{2}}}{2}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

= \frac{7}{2 ^{1 - \frac{1}{2}}}

数字相减:

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

= \frac{7}{2 ^{\frac{1}{2}}}

使用根式运算法则:

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

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

= \frac{7}{2}

\frac{7}{2}

有理化:

\frac{7 2}{2}

\frac{7}{2}

乘以共轭根式

\frac{2}{2}

= \frac{7 2}{2 2}

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{7 2}{2}

= \frac{7 2}{2}

= \frac{7 2}{2}

流行的例子

sinh (0.5)

sec (0.8)

csc(30)+tan(45)

csc (3 0^{\circ}) + tan (4 5^{\circ})

cos(pi/6)cos(pi/4)-sin(pi/6)sin(pi/4)

cos (\frac{π}{6}) cos (\frac{π}{4}) - sin (\frac{π}{6}) sin (\frac{π}{4})

sin^{2} (36 0^{\circ})