What is the general solution for pi/3 =3+2sin(2t) ?

The general solution for pi/3 =3+2sin(2t) is t=(-1.35311…)/2+pin,t= pi/2+(1.35311…)/2+pin

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pi/3 =3+2sin(2t)

\frac{π}{3} = 3 + 2 sin (2 t)

t = \frac{- 1.35311 \dots}{2} + πn, t = \frac{π}{2} + \frac{1.35311 \dots}{2} + πn

Solution steps

\frac{π}{3} = 3 + 2 sin (2 t)

Switch sides

3 + 2 sin (2 t) = \frac{π}{3}

Move

3

to the right side

2 sin (2 t) = \frac{π}{3} - 3

Divide both sides by

2

sin (2 t) = \frac{π - 9}{6}

Apply trig inverse properties

2 t = arcsin (\frac{π - 9}{6}) + 2 πn, 2 t = π + arcsin (- \frac{π - 9}{6}) + 2 πn

Solve

2 t = arcsin (\frac{π - 9}{6}) + 2 πn : t = \frac{arcsin ( \frac{π - 9}{6} )}{2} + πn

Solve

2 t = π + arcsin (- \frac{π - 9}{6}) + 2 πn : t = \frac{π}{2} + \frac{arcsin ( \frac{- π + 9}{6} )}{2} + πn

t = \frac{arcsin ( \frac{π - 9}{6} )}{2} + πn, t = \frac{π}{2} + \frac{arcsin ( \frac{- π + 9}{6} )}{2} + πn

Show solutions in decimal form

t = \frac{- 1.35311 \dots}{2} + πn, t = \frac{π}{2} + \frac{1.35311 \dots}{2} + πn

1 + sin (2 x) = 5 (sin (x) + cos (x))

x, y = I n [tan (5 x^{2} + 3 x + 2)]

cos (2 x) = \frac{3}{4} - 5 cos^{2} (x)

sin (x + \frac{π}{9}) = \frac{3}{2}

3 cos (2 θ) = 3 sin (θ)

What is the general solution for pi/3 =3+2sin(2t) ?
The general solution for pi/3 =3+2sin(2t) is t=(-1.35311…)/2+pin,t= pi/2+(1.35311…)/2+pin