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受欢迎的三角函数 >

cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi

解答

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

解答

x = \frac{11 π - 30}{6}, x = \frac{13 π - 30}{6}

求解步骤

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

化简

\frac{1}{2} 3 : \frac{3}{2}

\frac{1}{2} 3

分式相乘:

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

= \frac{1 \cdot 3}{2}

乘以:

1 \cdot 3 = 3

= \frac{3}{2}

cos (x + 5) = \frac{3}{2}

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}

x + 5 = \frac{π}{6} + 2 πn, x + 5 = \frac{11 π}{6} + 2 πn

x + 5 = \frac{π}{6} + 2 πn, x + 5 = \frac{11 π}{6} + 2 πn

解

x + 5 = \frac{π}{6} + 2 πn : x = \frac{π}{6} + 2 πn - 5

x + 5 = \frac{π}{6} + 2 πn

将

5

到右边

x + 5 = \frac{π}{6} + 2 πn

两边减去

5

x + 5 - 5 = \frac{π}{6} + 2 πn - 5

化简

x = \frac{π}{6} + 2 πn - 5

x = \frac{π}{6} + 2 πn - 5

解

x + 5 = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{6} + 2 πn - 5

x + 5 = \frac{11 π}{6} + 2 πn

将

5

到右边

x + 5 = \frac{11 π}{6} + 2 πn

两边减去

5

x + 5 - 5 = \frac{11 π}{6} + 2 πn - 5

化简

x = \frac{11 π}{6} + 2 πn - 5

x = \frac{11 π}{6} + 2 πn - 5

x = \frac{π}{6} + 2 πn - 5, x = \frac{11 π}{6} + 2 πn - 5

在

0 \leq x \leq 2 π

范围内的解

x = \frac{11 π - 30}{6}, x = \frac{13 π - 30}{6}

作图

流行的例子

cos^2(x)=3sin^2(x)

cos^{2} (x) = 3 sin^{2} (x)

2sec^2(x)+3sec(x)-2=0

2 sec^{2} (x) + 3 sec (x) - 2 = 0

- 4 arctan (x) = π

sin^2(x)=sin(x)cos(x)

sin^{2} (x) = sin (x) cos (x)

sin(x)=-(sqrt(3))/2 ,0<= x<= 2pi

sin (x) = - \frac{3}{2}, 0 \leq x \leq 2 π