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受欢迎的三角函数 >

sin(x)+cos(x)=1,-360<= x<= 360

解答

sin (x) + cos (x) = 1, - 36 0^{\circ} \leq x \leq 36 0^{\circ}

解答

x = 0, x = 9 0^{\circ}, x = 36 0^{\circ}, x = - 36 0^{\circ}, x = - 27 0^{\circ}

+1

弧度

x = 0, x = \frac{π}{2}, x = 2 π, x = - 2 π, x = - \frac{3 π}{2}

求解步骤

sin (x) + cos (x) = 1, - 36 0^{\circ} \leq x \leq 36 0^{\circ}

使用三角恒等式改写

sin (x) + cos (x)

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

sin (x) + cos (x)

改写为

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

使用以下普通恒等式:

cos (\frac{π}{4}) = \frac{1}{2}

使用以下普通恒等式:

sin (\frac{π}{4}) = \frac{1}{2}

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

使用角和恒等式:

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

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

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

2 sin (x + 4 5^{\circ}) = 1

两边除以

2

2 sin (x + 4 5^{\circ}) = 1

两边除以

2

\frac{2 sin ( x + 4 5 ^{\circ} )}{2} = \frac{1}{2}

化简

\frac{2 sin ( x + 4 5 ^{\circ} )}{2} = \frac{1}{2}

化简

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

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

约分:

2

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

化简

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

乘以共轭根式

\frac{2}{2}

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

1 \cdot 2 = 2

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{2}{2}

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

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

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

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

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 + 4 5^{\circ} = 4 5^{\circ} + 36 0^{\circ} n, x + 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

x + 4 5^{\circ} = 4 5^{\circ} + 36 0^{\circ} n, x + 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

解

x + 4 5^{\circ} = 4 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n

x + 4 5^{\circ} = 4 5^{\circ} + 36 0^{\circ} n

两边减去

4 5^{\circ}

x + 4 5^{\circ} - 4 5^{\circ} = 4 5^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

化简

x = 36 0^{\circ} n

解

x + 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 9 0^{\circ}

x + 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

将

4 5^{\circ}

到右边

x + 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

两边减去

4 5^{\circ}

x + 4 5^{\circ} - 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

化简

x + 4 5^{\circ} - 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

化简

x + 4 5^{\circ} - 4 5^{\circ} : x

x + 4 5^{\circ} - 4 5^{\circ}

同类项相加:

4 5^{\circ} - 4 5^{\circ} = 0

= x

化简

13 5^{\circ} + 36 0^{\circ} n - 4 5^{\circ} : 36 0^{\circ} n + 9 0^{\circ}

13 5^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

对同类项分组

= 36 0^{\circ} n - 4 5^{\circ} + 13 5^{\circ}

合并分式

- 4 5^{\circ} + 13 5^{\circ} : 9 0^{\circ}

使用法则

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

= \frac{- 18 0 ^{\circ} + 54 0 ^{\circ}}{4}

同类项相加:

- 18 0^{\circ} + 54 0^{\circ} = 36 0^{\circ}

= 9 0^{\circ}

约分:

2

= 9 0^{\circ}

= 36 0^{\circ} n + 9 0^{\circ}

x = 36 0^{\circ} n + 9 0^{\circ}

x = 36 0^{\circ} n + 9 0^{\circ}

x = 36 0^{\circ} n + 9 0^{\circ}

x = 36 0^{\circ} n, x = 36 0^{\circ} n + 9 0^{\circ}

在

- 36 0^{\circ} \leq x \leq 36 0^{\circ}

范围内的解

x = 0, x = 9 0^{\circ}, x = 36 0^{\circ}, x = - 36 0^{\circ}, x = - 27 0^{\circ}

作图

流行的例子

5 csc (θ) + 6 = 0

sin (x^{2}) = 1

cos(2θ)-sqrt(3)cos(θ)=0,0<= θ<2pi

cos (2 θ) - 3 cos (θ) = 0, 0 \leq θ < 2 π

2cos^2(θ)-7cos(θ)-4=0

2 cos^{2} (θ) - 7 cos (θ) - 4 = 0

sin(θ)= 3/10 ,sin(θ+pi/6)

sin (θ) = \frac{3}{10}, sin (θ + \frac{π}{6})