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受欢迎的三角函数 >

cos^2(x)sec(x)=1

解答

cos^{2} (x) sec (x) = 1

解答

x = 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n

求解步骤

cos^{2} (x) sec (x) = 1

两边减去

1

cos^{2} (x) sec (x) - 1 = 0

使用三角恒等式改写

- 1 + cos^{2} (x) sec (x)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= - 1 + cos^{2} (x) \frac{1}{cos ( x )}

cos^{2} (x) \frac{1}{cos ( x )} = cos (x)

cos^{2} (x) \frac{1}{cos ( x )}

分式相乘:

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

= \frac{1 \cdot cos ^{2} ( x )}{cos ( x )}

乘以:

1 \cdot cos^{2} (x) = cos^{2} (x)

= \frac{cos ^{2} ( x )}{cos ( x )}

约分:

cos (x)

= cos (x)

= - 1 + cos (x)

- 1 + cos (x) = 0

将

1

到右边

- 1 + cos (x) = 0

两边加上

1

- 1 + cos (x) + 1 = 0 + 1

化简

cos (x) = 1

cos (x) = 1

cos (x) = 1

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 = 0 + 2 πn

x = 0 + 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

作图

流行的例子

tan(x)=(9.3)/(7.5)

tan (x) = \frac{9.3}{7.5}

sin(α)+cos(α)=1

sin (α) + cos (α) = 1

2sin(θ)=sqrt(3)tan(θ)

2 sin (θ) = 3 tan (θ)

sin (θ) = - 0.78

4tan(θ)=5-tan(θ)

4 tan (θ) = 5 - tan (θ)