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受欢迎的三角函数 >

sqrt(5)sin(θ+0.4636)=1

解答

5 sin (θ + 0.4636) = 1

解答

θ = 0.46364 \dots + 2 πn - 0.4636, θ = π - 0.46364 \dots + 2 πn - 0.4636

+1

度数

θ = 0.00272 \dots^{\circ} + 36 0^{\circ} n, θ = 126.87262 \dots^{\circ} + 36 0^{\circ} n

求解步骤

5 sin (θ + 0.4636) = 1

两边除以

5

5 sin (θ + 0.4636) = 1

两边除以

5

\frac{5 sin ( θ + 0.4636 )}{5} = \frac{1}{5}

化简

\frac{5 sin ( θ + 0.4636 )}{5} = \frac{1}{5}

化简

\frac{5 sin ( θ + 0.4636 )}{5} : sin (θ + 0.4636)

\frac{5 sin ( θ + 0.4636 )}{5}

约分:

5

= sin (θ + 0.4636)

化简

\frac{1}{5} : \frac{5}{5}

\frac{1}{5}

乘以共轭根式

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

使用根式运算法则:

a a = a

55 = 5

= 5

= \frac{5}{5}

sin (θ + 0.4636) = \frac{5}{5}

sin (θ + 0.4636) = \frac{5}{5}

sin (θ + 0.4636) = \frac{5}{5}

使用反三角函数性质

sin (θ + 0.4636) = \frac{5}{5}

sin (θ + 0.4636) = \frac{5}{5}

的通解

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

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn, θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn, θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn

解

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn : θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn

化简

arcsin (\frac{5}{5}) + 2 πn : arcsin (\frac{1}{5}) + 2 πn

arcsin (\frac{5}{5}) + 2 πn

\frac{5}{5} = \frac{1}{5}

\frac{5}{5}

使用根式运算法则:

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

5 = 5^{\frac{1}{2}}

= \frac{5 ^{\frac{1}{2}}}{5}

使用指数法则:

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

\frac{5 ^{\frac{1}{2}}}{5 ^{1}} = \frac{1}{5 ^{1 - \frac{1}{2}}}

= \frac{1}{5 ^{1 - \frac{1}{2}}}

数字相减:

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

= \frac{1}{5 ^{\frac{1}{2}}}

使用根式运算法则:

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

5^{\frac{1}{2}} = 5

= \frac{1}{5}

= arcsin (\frac{1}{5}) + 2 πn

θ + 0.4636 = arcsin (\frac{1}{5}) + 2 πn

将

0.4636

到右边

θ + 0.4636 = arcsin (\frac{1}{5}) + 2 πn

两边减去

0.4636

θ + 0.4636 - 0.4636 = arcsin (\frac{1}{5}) + 2 πn - 0.4636

化简

θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636

解

θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn : θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn

化简

π - arcsin (\frac{5}{5}) + 2 πn : π - arcsin (\frac{1}{5}) + 2 πn

π - arcsin (\frac{5}{5}) + 2 πn

\frac{5}{5} = \frac{1}{5}

\frac{5}{5}

使用根式运算法则:

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

5 = 5^{\frac{1}{2}}

= \frac{5 ^{\frac{1}{2}}}{5}

使用指数法则:

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

\frac{5 ^{\frac{1}{2}}}{5 ^{1}} = \frac{1}{5 ^{1 - \frac{1}{2}}}

= \frac{1}{5 ^{1 - \frac{1}{2}}}

数字相减:

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

= \frac{1}{5 ^{\frac{1}{2}}}

使用根式运算法则:

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

5^{\frac{1}{2}} = 5

= \frac{1}{5}

= π - arcsin (\frac{1}{5}) + 2 πn

θ + 0.4636 = π - arcsin (\frac{1}{5}) + 2 πn

将

0.4636

到右边

θ + 0.4636 = π - arcsin (\frac{1}{5}) + 2 πn

两边减去

0.4636

θ + 0.4636 - 0.4636 = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

化简

θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636, θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

以小数形式表示解

θ = 0.46364 \dots + 2 πn - 0.4636, θ = π - 0.46364 \dots + 2 πn - 0.4636

作图

流行的例子

0= 20/3 sin(10t)+5cos(10t)

0 = \frac{20}{3} sin (10 t) + 5 cos (10 t)

solvefor y,arctan(y)=(t^2)/2

so l v e f or y, arctan (y) = \frac{t ^{2}}{2}

cos (- x) = 0

2 tan^{2} (x) + 1 = 0

solvefor y,arctan(y)=(x^3)/3-2x+c

so l v e f or y, arctan (y) = \frac{x ^{3}}{3} - 2 x + c