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7sin(x+5)=1

解答

7 sin (x + 5) = 1

解答

x = 0.14334 \dots + 2 πn - 5, x = π - 0.14334 \dots + 2 πn - 5

+1

度数

x = - 278.26568 \dots^{\circ} + 36 0^{\circ} n, x = - 114.69210 \dots^{\circ} + 36 0^{\circ} n

求解步骤

7 sin (x + 5) = 1

两边除以

7

7 sin (x + 5) = 1

两边除以

7

\frac{7 sin ( x + 5 )}{7} = \frac{1}{7}

化简

sin (x + 5) = \frac{1}{7}

sin (x + 5) = \frac{1}{7}

使用反三角函数性质

sin (x + 5) = \frac{1}{7}

sin (x + 5) = \frac{1}{7}

的通解

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

x + 5 = arcsin (\frac{1}{7}) + 2 πn, x + 5 = π - arcsin (\frac{1}{7}) + 2 πn

x + 5 = arcsin (\frac{1}{7}) + 2 πn, x + 5 = π - arcsin (\frac{1}{7}) + 2 πn

解

x + 5 = arcsin (\frac{1}{7}) + 2 πn : x = arcsin (\frac{1}{7}) + 2 πn - 5

x + 5 = arcsin (\frac{1}{7}) + 2 πn

将

5

到右边

x + 5 = arcsin (\frac{1}{7}) + 2 πn

两边减去

5

x + 5 - 5 = arcsin (\frac{1}{7}) + 2 πn - 5

化简

x = arcsin (\frac{1}{7}) + 2 πn - 5

x = arcsin (\frac{1}{7}) + 2 πn - 5

解

x + 5 = π - arcsin (\frac{1}{7}) + 2 πn : x = π - arcsin (\frac{1}{7}) + 2 πn - 5

x + 5 = π - arcsin (\frac{1}{7}) + 2 πn

将

5

到右边

x + 5 = π - arcsin (\frac{1}{7}) + 2 πn

两边减去

5

x + 5 - 5 = π - arcsin (\frac{1}{7}) + 2 πn - 5

化简

x = π - arcsin (\frac{1}{7}) + 2 πn - 5

x = π - arcsin (\frac{1}{7}) + 2 πn - 5

x = arcsin (\frac{1}{7}) + 2 πn - 5, x = π - arcsin (\frac{1}{7}) + 2 πn - 5

以小数形式表示解

x = 0.14334 \dots + 2 πn - 5, x = π - 0.14334 \dots + 2 πn - 5

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2 sin (x) tan (2 x) - 3 tan (2 x) = 0

tan (x) = \frac{12}{8}

cos(2t)-cos(t)=-0.5,0<= t<= 2pi

cos (2 t) - cos (t) = - 0.5, 0 \leq t \leq 2 π

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