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受欢迎的三角函数 >

cos(x)=sqrt(2)cos(45+x)

解答

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

解答

x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

+1

弧度

x = 0 + 2 πn, x = π + 2 πn

求解步骤

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

使用三角恒等式改写

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

使用三角恒等式改写

cos (4 5^{\circ} + x)

使用角和恒等式:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (4 5^{\circ}) cos (x) - sin (4 5^{\circ}) sin (x)

化简

cos (4 5^{\circ}) cos (x) - sin (4 5^{\circ}) sin (x) : \frac{2 cos ( x ) - 2 sin ( x )}{2}

cos (4 5^{\circ}) cos (x) - sin (4 5^{\circ}) sin (x)

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

cos (4 5^{\circ}) cos (x)

化简

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

cos (4 5^{\circ})

使用以下普通恒等式:

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

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{2}{2} cos (x)

分式相乘:

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

= \frac{2 cos ( x )}{2}

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

sin (4 5^{\circ}) sin (x)

化简

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

sin (4 5^{\circ})

使用以下普通恒等式:

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

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}

= \frac{2}{2} sin (x)

分式相乘:

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

= \frac{2 sin ( x )}{2}

= \frac{2 cos ( x )}{2} - \frac{2 sin ( x )}{2}

使用法则

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

= \frac{2 cos ( x ) - 2 sin ( x )}{2}

= \frac{2 cos ( x ) - 2 sin ( x )}{2}

cos (x) = 2 \frac{2 cos ( x ) - 2 sin ( x )}{2}

化简

2 \frac{2 cos ( x ) - 2 sin ( x )}{2} : cos (x) - sin (x)

2 \frac{2 cos ( x ) - 2 sin ( x )}{2}

\frac{2 cos ( x ) - 2 sin ( x )}{2} = \frac{cos ( x ) - sin ( x )}{2}

\frac{2 cos ( x ) - 2 sin ( x )}{2}

因式分解出通项

2

= \frac{2 ( cos ( x ) - sin ( x ) )}{2}

消掉

\frac{2 ( cos ( x ) - sin ( x ) )}{2} : \frac{cos ( x ) - sin ( x )}{2}

\frac{2 ( cos ( x ) - sin ( x ) )}{2}

使用根式运算法则:

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

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

= \frac{2 ^{\frac{1}{2}} ( cos ( x ) - sin ( x ) )}{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{cos ( x ) - sin ( x )}{2 ^{1 - \frac{1}{2}}}

数字相减:

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

= \frac{cos ( x ) - sin ( x )}{2 ^{\frac{1}{2}}}

使用根式运算法则:

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

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

= \frac{cos ( x ) - sin ( x )}{2}

= \frac{cos ( x ) - sin ( x )}{2}

= 2 \frac{cos ( x ) - sin ( x )}{2}

分式相乘:

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

= \frac{( cos ( x ) - sin ( x ) ) 2}{2}

约分:

2

= cos (x) - sin (x)

cos (x) = cos (x) - sin (x)

cos (x) = cos (x) - sin (x)

两边减去

cos (x) - sin (x)

sin (x) = 0

sin (x) = 0

的通解

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}

x = 0 + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

x = 0 + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解

x = 0 + 36 0^{\circ} n : x = 36 0^{\circ} n

x = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

x = 36 0^{\circ} n

x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

作图

流行的例子

2 sin (θ) = 1.124

cos (θ) = - 0.11

tan(θ)=(sqrt(2))/2

tan (θ) = \frac{2}{2}

tan^{2} (θ) - 16 = 0

(0.5)(9.8)=(0.45)(9.8)sin(θ)

(0.5) (9.8) = (0.45) (9.8) sin (θ)