sin(θ)=-3/5 ,cos(θ)= 4/5 ,tan(θ),cot(θ)

解答

sin (θ) = - \frac{3}{5}, cos (θ) = \frac{4}{5}, tan (θ), cot (θ)

θ \in R 无解

求解步骤

sin (θ) = - \frac{3}{5}, cos (θ) = \frac{4}{5}, tan (θ), cot (θ)

使用反三角函数性质

sin (θ) = - \frac{3}{5}

sin (θ) = - \frac{3}{5}

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

θ = arcsin (- \frac{3}{5}) + 2 πn, θ = π + arcsin (\frac{3}{5}) + 2 πn

θ = arcsin (- \frac{3}{5}) + 2 πn, θ = π + arcsin (\frac{3}{5}) + 2 πn

在

cos (θ) = \frac{4}{5}

范围内的解

θ \in R 无解

cos (6 0^{\circ} - x) = 1

cos (t) - sin (t) = 0

sin (x) - cos (x) = \frac{1}{3}

tan^{2} (x) = sec (x) - 1, 0 \leq x \leq 2 π

sin^{2} (θ) = 2 sin^{2} (\frac{θ}{2})