csc(θ)=(sqrt(34))/3 ,cos(θ)>0

解答

csc (θ) = \frac{34}{3}, cos (θ) > 0

θ \in R 无解

求解步骤

csc (θ) = \frac{34}{3}, cos (θ) > 0

使用反三角函数性质

csc (θ) = \frac{34}{3}

csc (θ) = \frac{34}{3}

的通解

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

θ = arccsc (\frac{34}{3}) + 2 πn, θ = π - arccsc (\frac{34}{3}) + 2 πn

θ = arccsc (\frac{34}{3}) + 2 πn, θ = π - arccsc (\frac{34}{3}) + 2 πn

在

cos (θ) > 0

范围内的解

θ \in R 无解

sin^{2} (x) + 4 cos^{2} (x) = 1

5 sin^{2} (x) = 9 tan (x)

cos (θ) = \frac{5}{4}

csc^{2} (x) = 4 cot^{2} (x)

3 cos (θ) = 2, 1