What is the general solution for sec((3θ)/2)=-2,0<= θ<2pi ?

The general solution for sec((3θ)/2)=-2,0<= θ<2pi is θ=(4pi)/9 ,θ=(8pi)/9 ,θ=(16pi)/9

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sec((3θ)/2)=-2,0<= θ<2pi

sec (\frac{3 θ}{2}) = - 2, 0 \leq θ < 2 π

θ = \frac{4 π}{9}, θ = \frac{8 π}{9}, θ = \frac{16 π}{9}

Solution steps

sec (\frac{3 θ}{2}) = - 2, 0 \leq θ < 2 π

General solutions for

sec (\frac{3 θ}{2}) = - 2

\frac{3 θ}{2} = \frac{2 π}{3} + 2 πn, \frac{3 θ}{2} = \frac{4 π}{3} + 2 πn

Solve

\frac{3 θ}{2} = \frac{2 π}{3} + 2 πn : θ = \frac{4 π}{9} + \frac{4 πn}{3}

Solve

\frac{3 θ}{2} = \frac{4 π}{3} + 2 πn : θ = \frac{8 π}{9} + \frac{4 πn}{3}

θ = \frac{4 π}{9} + \frac{4 πn}{3}, θ = \frac{8 π}{9} + \frac{4 πn}{3}

Solutions for the range

0 \leq θ < 2 π

θ = \frac{4 π}{9}, θ = \frac{8 π}{9}, θ = \frac{16 π}{9}

tan (x - \frac{π}{6}) = 3

- 5 cos (5 x) = 0

2 sin (x) tan (x) + 5 = 4 sec (x)

cos^{2} (x) - cos (x) - 2 = 0, 0 \leq x \leq 2 π

cos^{4} (x) - 1 = 0

What is the general solution for sec((3θ)/2)=-2,0<= θ<2pi ?
The general solution for sec((3θ)/2)=-2,0<= θ<2pi is θ=(4pi)/9 ,θ=(8pi)/9 ,θ=(16pi)/9