sin(x)= 4/5 , pi/2 <= 0<pi,sin(2x)

解答

sin (x) = \frac{4}{5}, \frac{π}{2} \leq 0 < π, sin (2 x)

x \in R 无解

求解步骤

sin (x) = \frac{4}{5}, \frac{π}{2} \leq 0 < π, sin (2 x)

使用反三角函数性质

sin (x) = \frac{4}{5}

sin (x) = \frac{4}{5}

的通解

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

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

在

\frac{π}{2} \leq 0 < π

范围内的解

x \in R 无解

2 cos^{2} (θ) - 3 cos (θ) + 1 = 0, \frac{3 π}{2} < θ < 2 π

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

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

4 cos (2 t) = 2

tan (θ) = \frac{10}{5.32}