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受欢迎的三角函数 >

cos(2θ)+sin^2(θ)=0

解答

cos (2 θ) + sin^{2} (θ) = 0

解答

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

+1

度数

θ = 9 0^{\circ} + 36 0^{\circ} n, θ = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

cos (2 θ) + sin^{2} (θ) = 0

使用三角恒等式改写

cos (2 θ) + sin^{2} (θ)

使用倍角公式:

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

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

= cos (2 θ) - (cos (2 θ) - cos^{2} (θ))

化简

cos (2 θ) - (cos (2 θ) - cos^{2} (θ)) : cos^{2} (θ)

cos (2 θ) - (cos (2 θ) - cos^{2} (θ))

- (cos (2 θ) - cos^{2} (θ)) : - cos (2 θ) + cos^{2} (θ)

- (cos (2 θ) - cos^{2} (θ))

打开括号

= - (cos (2 θ)) - (- cos^{2} (θ))

使用加减运算法则

- (- a) = a, - (a) = - a

= - cos (2 θ) + cos^{2} (θ)

= cos (2 θ) - cos (2 θ) + cos^{2} (θ)

同类项相加:

cos (2 θ) - cos (2 θ) = 0

= cos^{2} (θ)

= cos^{2} (θ)

cos^{2} (θ) = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

cos (θ) = 0

cos (θ) = 0

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}

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

作图

流行的例子

tan^2(x)+tan(x)=0,0<= x<2pi

tan^{2} (x) + tan (x) = 0, 0 \leq x < 2 π

csc (x) - 1 = 0

cos(2x)+5cos(x)+3=0

cos (2 x) + 5 cos (x) + 3 = 0

2 cos (θ) = 1

sin(x+pi/6)-sin(x-pi/6)= 1/2

sin (x + \frac{π}{6}) - sin (x - \frac{π}{6}) = \frac{1}{2}