sin(t)= 7/9 ,sin(2t)

解答

sin (t) = \frac{7}{9}, sin (2 t)

t \in R 无解

求解步骤

sin (t) = \frac{7}{9}, sin (2 t)

使用反三角函数性质

sin (t) = \frac{7}{9}

sin (t) = \frac{7}{9}

的通解

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

t = arcsin (\frac{7}{9}) + 2 πn, t = π - arcsin (\frac{7}{9}) + 2 πn

t = arcsin (\frac{7}{9}) + 2 πn, t = π - arcsin (\frac{7}{9}) + 2 πn

在

sin (2 t)

范围内的解

t \in R 无解

\frac{8}{17} = sin (2 x)

sec (2 x) + tan (2 x) = 2

sec (2 x) + tan (2 x) = 9

tan (4 x) - tan (2 x) = 0

so l v e f or t, sin (t) + 2 sin (2 t) = 0