sec(θ)=-sqrt(5)

解答

sec (θ) = - 5

θ = 2.03444 \dots + 2 πn, θ = - 2.03444 \dots + 2 πn

度数

θ = 116.56505 \dots^{\circ} + 36 0^{\circ} n, θ = - 116.56505 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sec (θ) = - 5

使用反三角函数性质

sec (θ) = - 5

sec (θ) = - 5

的通解

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

θ = arcsec (- 5) + 2 πn, θ = - arcsec (- 5) + 2 πn

θ = arcsec (- 5) + 2 πn, θ = - arcsec (- 5) + 2 πn

以小数形式表示解

θ = 2.03444 \dots + 2 πn, θ = - 2.03444 \dots + 2 πn

sin (2 x) - 3 cos (x) = 0

5 sin^{2} (x) - sin (x) = 0

3 sin^{2} (2 x) + 7 cos (2 x) - 3 = 0

3 cos^{2} (θ) - 1 = 2 cos (θ)

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