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受欢迎的三角函数 >

sin(x)sec(x)=2sin(x),0<= x<= 2pi

解答

sin (x) sec (x) = 2 sin (x), 0 \leq x \leq 2 π

解答

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

+1

度数

x = 0^{\circ}, x = 18 0^{\circ}, x = 36 0^{\circ}, x = 6 0^{\circ}, x = 30 0^{\circ}

求解步骤

sin (x) sec (x) = 2 sin (x), 0 \leq x \leq 2 π

两边减去

2 sin (x)

sin (x) sec (x) - 2 sin (x) = 0

分解

sin (x) sec (x) - 2 sin (x) : sin (x) (sec (x) - 2)

sin (x) sec (x) - 2 sin (x)

因式分解出通项

sin (x)

= sin (x) (sec (x) - 2)

sin (x) (sec (x) - 2) = 0

分别求解每个部分

sin (x) = 0 or sec (x) - 2 = 0

sin (x) = 0, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

sin (x) = 0, 0 \leq x \leq 2 π

sin (x) = 0

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = 0, x = π, x = 2 π

sec (x) - 2 = 0, 0 \leq x \leq 2 π : x = \frac{π}{3}, x = \frac{5 π}{3}

sec (x) - 2 = 0, 0 \leq x \leq 2 π

将

2

到右边

sec (x) - 2 = 0

两边加上

2

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

化简

sec (x) = 2

sec (x) = 2

sec (x) = 2

的通解

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{π}{3}, x = \frac{5 π}{3}

合并所有解

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

作图

流行的例子

3cos^2(y)-1=cos(y)+cos^2(y),pi<= y<= 2pi

3 cos^{2} (y) - 1 = cos (y) + cos^{2} (y), π \leq y \leq 2 π

6tanh^2(x)+5sech(x)-7=0

6 tanh^{2} (x) + 5 sech (x) - 7 = 0

2sin(x)+sqrt(2)=0,0<= x<= 2pi

2 sin (x) + 2 = 0, 0 \leq x \leq 2 π

2cos^2(x)+3cos(x)=2,0<= x<= 2pi

2 cos^{2} (x) + 3 cos (x) = 2, 0 \leq x \leq 2 π

cos (θ) = \frac{7}{11}