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受欢迎的三角函数 >

(cos(θ))(cos(θ))+1=(sin(θ))(sin(θ))

解答

(cos (θ)) (cos (θ)) + 1 = (sin (θ)) (sin (θ))

解答

θ = \frac{π}{2} + πn

+1

度数

θ = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

(cos (θ)) (cos (θ)) + 1 = (sin (θ)) (sin (θ))

两边减去

sin (θ) sin (θ)

cos^{2} (θ) + 1 - sin^{2} (θ) = 0

使用三角恒等式改写

cos^{2} (θ) + 1 - sin^{2} (θ)

使用倍角公式:

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

= 1 + cos (2 θ)

1 + cos (2 θ) = 0

将

1

到右边

1 + cos (2 θ) = 0

两边减去

1

1 + cos (2 θ) - 1 = 0 - 1

化简

cos (2 θ) = - 1

cos (2 θ) = - 1

cos (2 θ) = - 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}

2 θ = π + 2 πn

2 θ = π + 2 πn

解

2 θ = π + 2 πn : θ = \frac{π}{2} + πn

2 θ = π + 2 πn

两边除以

2

2 θ = π + 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{π}{2} + \frac{2 πn}{2}

化简

θ = \frac{π}{2} + πn

θ = \frac{π}{2} + πn

θ = \frac{π}{2} + πn

作图

流行的例子

1+4tan^2(θ)=sec^2(θ)

1 + 4 tan^{2} (θ) = sec^{2} (θ)

3csc(x)=4+csc(x)

3 csc (x) = 4 + csc (x)

tan (θ) = - \frac{8}{15}

4 cos (t) = 0

7sec^3(x)+16sec^2(x)+11sec(x)+2=0

7 sec^{3} (x) + 16 sec^{2} (x) + 11 sec (x) + 2 = 0