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受欢迎的三角函数 >

-9.81+5(32.17)(12/2)sin(θ)=0

解答

- 9.81 + 5 (32.17) (\frac{12}{2}) sin (θ) = 0

解答

θ = 0.01016 \dots + 2 πn, θ = π - 0.01016 \dots + 2 πn

+1

度数

θ = 0.58240 \dots^{\circ} + 36 0^{\circ} n, θ = 179.41759 \dots^{\circ} + 36 0^{\circ} n

求解步骤

- 9.81 + 5 (32.17) (\frac{12}{2}) sin (θ) = 0

5 \cdot 32.17 \cdot \frac{12}{2} sin (θ) = 965.1 sin (θ)

5 \cdot 32.17 \cdot \frac{12}{2} sin (θ)

分式相乘:

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

= 32.17 \cdot \frac{12 \cdot 5 sin ( θ )}{2}

化简

\frac{12 \cdot 5 sin ( θ )}{2} : 30 sin (θ)

\frac{12 \cdot 5 sin ( θ )}{2}

数字相乘:

12 \cdot 5 = 60

= \frac{60 sin ( θ )}{2}

数字相除:

\frac{60}{2} = 30

= 30 sin (θ)

= 30 \cdot 32.17 sin (θ)

数字相乘:

32.17 \cdot 30 = 965.1

= 965.1 sin (θ)

- 9.81 + 965.1 sin (θ) = 0

在两边乘以

100

- 9.81 + 965.1 sin (θ) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- 9.81 \cdot 100 + 965.1 sin (θ) \cdot 100 = 0 \cdot 100

整理后得

- 981 + 96510 sin (θ) = 0

- 981 + 96510 sin (θ) = 0

将

981

到右边

- 981 + 96510 sin (θ) = 0

两边加上

981

- 981 + 96510 sin (θ) + 981 = 0 + 981

化简

96510 sin (θ) = 981

96510 sin (θ) = 981

两边除以

96510

96510 sin (θ) = 981

两边除以

96510

\frac{96510 sin ( θ )}{96510} = \frac{981}{96510}

化简

sin (θ) = \frac{327}{32170}

sin (θ) = \frac{327}{32170}

使用反三角函数性质

sin (θ) = \frac{327}{32170}

sin (θ) = \frac{327}{32170}

的通解

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

θ = arcsin (\frac{327}{32170}) + 2 πn, θ = π - arcsin (\frac{327}{32170}) + 2 πn

θ = arcsin (\frac{327}{32170}) + 2 πn, θ = π - arcsin (\frac{327}{32170}) + 2 πn

以小数形式表示解

θ = 0.01016 \dots + 2 πn, θ = π - 0.01016 \dots + 2 πn

作图

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