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受欢迎的三角函数 >

(tan(θ)-1)(sec(θ)-1)=0

解答

(tan (θ) - 1) (sec (θ) - 1) = 0

解答

θ = \frac{π}{4} + πn, θ = 2 πn

+1

度数

θ = 4 5^{\circ} + 18 0^{\circ} n, θ = 0^{\circ} + 36 0^{\circ} n

求解步骤

(tan (θ) - 1) (sec (θ) - 1) = 0

分别求解每个部分

tan (θ) - 1 = 0 or sec (θ) - 1 = 0

tan (θ) - 1 = 0 : θ = \frac{π}{4} + πn

tan (θ) - 1 = 0

将

1

到右边

tan (θ) - 1 = 0

两边加上

1

tan (θ) - 1 + 1 = 0 + 1

化简

tan (θ) = 1

tan (θ) = 1

tan (θ) = 1

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

sec (θ) - 1 = 0 : θ = 2 πn

sec (θ) - 1 = 0

将

1

到右边

sec (θ) - 1 = 0

两边加上

1

sec (θ) - 1 + 1 = 0 + 1

化简

sec (θ) = 1

sec (θ) = 1

sec (θ) = 1

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}

θ = 0 + 2 πn

θ = 0 + 2 πn

解

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn

合并所有解

θ = \frac{π}{4} + πn, θ = 2 πn

作图

流行的例子

cos (x) = - 2

cos(x)+sin(x)=1

cos (x) + sin (x) = 1

2sin(x)=-sqrt(2)

2 sin (x) = - 2

solvefor x,y=sin(x)

so l v e f or x, y = sin (x)

sqrt(3)sec(x)=2

3 sec (x) = 2