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受欢迎的三角函数 >

sin(θ)+cos(θ)=0.46

解答

sin (θ) + cos (θ) = 0.46

解答

θ = 0.33129 \dots + 2 πn - \frac{π}{4}, θ = π - 0.33129 \dots + 2 πn - \frac{π}{4}

+1

度数

θ = - 26.01811 \dots^{\circ} + 36 0^{\circ} n, θ = 116.01811 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin (θ) + cos (θ) = 0.46

使用三角恒等式改写

sin (θ) + cos (θ)

sin (θ) + cos (θ) = 2 sin (θ + \frac{π}{4})

sin (θ) + cos (θ)

改写为

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

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 (\frac{π}{4}) sin (θ) + sin (\frac{π}{4}) cos (θ))

使用角和恒等式:

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

= 2 sin (θ + \frac{π}{4})

= 2 sin (θ + \frac{π}{4})

2 sin (θ + \frac{π}{4}) = 0.46

两边除以

2

2 sin (θ + \frac{π}{4}) = 0.46

两边除以

2

\frac{2 sin ( θ + \frac{π}{4} )}{2} = \frac{0.46}{2}

化简

\frac{2 sin ( θ + \frac{π}{4} )}{2} = \frac{0.46}{2}

化简

\frac{2 sin ( θ + \frac{π}{4} )}{2} : sin (θ + \frac{π}{4})

\frac{2 sin ( θ + \frac{π}{4} )}{2}

约分:

2

= sin (θ + \frac{π}{4})

化简

\frac{0.46}{2} : 0.32526 \dots

\frac{0.46}{2}

转换为小数形式

2 = 1.41421 \dots

= \frac{0.46}{1.41421 \dots}

数字相除:

\frac{0.46}{1.41421 \dots} = 0.32526 \dots

= 0.32526 \dots

sin (θ + \frac{π}{4}) = 0.32526 \dots

sin (θ + \frac{π}{4}) = 0.32526 \dots

sin (θ + \frac{π}{4}) = 0.32526 \dots

使用反三角函数性质

sin (θ + \frac{π}{4}) = 0.32526 \dots

sin (θ + \frac{π}{4}) = 0.32526 \dots

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

θ + \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn, θ + \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn

θ + \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn, θ + \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn

解

θ + \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn : θ = arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

θ + \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn

将

\frac{π}{4}

到右边

θ + \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn

两边减去

\frac{π}{4}

θ + \frac{π}{4} - \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

化简

θ = arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

θ = arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

解

θ + \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn : θ = π - arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

θ + \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn

将

\frac{π}{4}

到右边

θ + \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn

两边减去

\frac{π}{4}

θ + \frac{π}{4} - \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

化简

θ = π - arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

θ = π - arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

θ = arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}, θ = π - arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

以小数形式表示解

θ = 0.33129 \dots + 2 πn - \frac{π}{4}, θ = π - 0.33129 \dots + 2 πn - \frac{π}{4}

作图

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