# Find the general solution of 4cosec (2x + 1) = 9

• June 13th 2006, 07:27 PM
Kiwigirl
Find the general solution of 4cosec (2x + 1) = 9
Find the general solution of the following trigonometric equation:

4cosec (2x + 1) = 9
• June 13th 2006, 08:31 PM
Soroban
Hello, Kiwigirl!

Quote:

Find the general solution of: $4\csc(2x + 1) \;= \;9$
Divide by 4: . $\csc(2x + 1) \;= \;\frac{9}{4}$

Take reciprocals: . $\sin(2x + 1) \;= \;\frac{4}{9}$

Then: . $2x + 1 \;= \;\arcsin\left(\frac{4}{9}\right) + 2\pi n$

. . . $2x \;= \;\arcsin\left(\frac{4}{9}\right) + 2\pi n - 1$

. . . $x \;= \;\frac{1}{2}\arcsin\left(\frac{4}{9}\right) + \pi n - \frac{1}{2}$