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受欢迎的三角函数 >

cos(3.7x+5.2)=0

解答

cos (3.7 x + 5.2) = 0

解答

x = \frac{5 π}{37} + \frac{20 πn}{37} - \frac{52}{37}, x = \frac{15 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

度数

x = - 56.19947 \dots^{\circ} + 97.29729 \dots^{\circ} n, x = - 7.55082 \dots^{\circ} + 97.29729 \dots^{\circ} n

求解步骤

cos (3.7 x + 5.2) = 0

cos (3.7 x + 5.2) = 0

的通解

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

3.7 x + 5.2 = \frac{π}{2} + 2 πn, 3.7 x + 5.2 = \frac{3 π}{2} + 2 πn

3.7 x + 5.2 = \frac{π}{2} + 2 πn, 3.7 x + 5.2 = \frac{3 π}{2} + 2 πn

解

3.7 x + 5.2 = \frac{π}{2} + 2 πn : x = \frac{5 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

3.7 x + 5.2 = \frac{π}{2} + 2 πn

在两边乘以

10

3.7 x + 5.2 = \frac{π}{2} + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

3.7 x \cdot 10 + 5.2 \cdot 10 = \frac{π}{2} \cdot 10 + 2 πn \cdot 10

整理后得

37 x + 52 = 5 π + 20 πn

37 x + 52 = 5 π + 20 πn

将

52

到右边

37 x + 52 = 5 π + 20 πn

两边减去

52

37 x + 52 - 52 = 5 π + 20 πn - 52

化简

37 x = 5 π + 20 πn - 52

37 x = 5 π + 20 πn - 52

两边除以

37

37 x = 5 π + 20 πn - 52

两边除以

37

\frac{37 x}{37} = \frac{5 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

化简

x = \frac{5 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

x = \frac{5 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

解

3.7 x + 5.2 = \frac{3 π}{2} + 2 πn : x = \frac{15 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

3.7 x + 5.2 = \frac{3 π}{2} + 2 πn

在两边乘以

10

3.7 x + 5.2 = \frac{3 π}{2} + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

3.7 x \cdot 10 + 5.2 \cdot 10 = \frac{3 π}{2} \cdot 10 + 2 πn \cdot 10

整理后得

37 x + 52 = 15 π + 20 πn

37 x + 52 = 15 π + 20 πn

将

52

到右边

37 x + 52 = 15 π + 20 πn

两边减去

52

37 x + 52 - 52 = 15 π + 20 πn - 52

化简

37 x = 15 π + 20 πn - 52

37 x = 15 π + 20 πn - 52

两边除以

37

37 x = 15 π + 20 πn - 52

两边除以

37

\frac{37 x}{37} = \frac{15 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

化简

x = \frac{15 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

x = \frac{15 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

x = \frac{5 π}{37} + \frac{20 πn}{37} - \frac{52}{37}, x = \frac{15 π}{37} + \frac{20 πn}{37} - \frac{52}{37}

作图

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