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受欢迎的三角函数 >

sqrt(7)sin(θ)-1=0

解答

7 sin (θ) - 1 = 0

解答

θ = 0.38759 \dots + 2 πn, θ = π - 0.38759 \dots + 2 πn

+1

度数

θ = 22.20765 \dots^{\circ} + 36 0^{\circ} n, θ = 157.79234 \dots^{\circ} + 36 0^{\circ} n

求解步骤

7 sin (θ) - 1 = 0

将

1

到右边

7 sin (θ) - 1 = 0

两边加上

1

7 sin (θ) - 1 + 1 = 0 + 1

化简

7 sin (θ) = 1

7 sin (θ) = 1

两边除以

7

7 sin (θ) = 1

两边除以

7

\frac{7 sin ( θ )}{7} = \frac{1}{7}

化简

\frac{7 sin ( θ )}{7} = \frac{1}{7}

化简

\frac{7 sin ( θ )}{7} : sin (θ)

\frac{7 sin ( θ )}{7}

约分:

7

= sin (θ)

化简

\frac{1}{7} : \frac{7}{7}

\frac{1}{7}

乘以共轭根式

\frac{7}{7}

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

1 \cdot 7 = 7

77 = 7

77

使用根式运算法则:

a a = a

77 = 7

= 7

= \frac{7}{7}

sin (θ) = \frac{7}{7}

sin (θ) = \frac{7}{7}

sin (θ) = \frac{7}{7}

使用反三角函数性质

sin (θ) = \frac{7}{7}

sin (θ) = \frac{7}{7}

的通解

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

θ = arcsin (\frac{7}{7}) + 2 πn, θ = π - arcsin (\frac{7}{7}) + 2 πn

θ = arcsin (\frac{7}{7}) + 2 πn, θ = π - arcsin (\frac{7}{7}) + 2 πn

以小数形式表示解

θ = 0.38759 \dots + 2 πn, θ = π - 0.38759 \dots + 2 πn

作图

流行的例子

sin(3θ)=-1/(sqrt(2))

sin (3 θ) = - \frac{1}{2}

2sin(x)-cot(x)-csc(x)=0

2 sin (x) - cot (x) - csc (x) = 0

(-tan^2(x))/2 =cos^2(x)-1

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

sin (a) = \frac{π}{4}

sin (x - \frac{π}{2}) = 0