What is the general solution for solvefor y,t=2cot(60y+30) ?

The general solution for solvefor y,t=2cot(60y+30) is y=(3arccot(t/2))/(180)+3n-1/2

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solvefor y,t=2cot(60y+30)

solve for

y, t = 2 cot (6 0^{\circ} y + 3 0^{\circ})

y = \frac{3 arccot ( \frac{t}{2} )}{18 0 ^{\circ}} + 3 n - \frac{1}{2}

Solution steps

t = 2 cot (6 0^{\circ} y + 3 0^{\circ})

Switch sides

2 cot (\frac{π}{3} y + \frac{π}{6}) = t

Divide both sides by

2

cot (\frac{π}{3} y + \frac{π}{6}) = \frac{t}{2}

Apply trig inverse properties

\frac{π}{3} y + \frac{π}{6} = arccot (\frac{t}{2}) + πn

Solve

6 0^{\circ} y + 3 0^{\circ} = arccot (\frac{t}{2}) + 18 0^{\circ} n : y = \frac{3 arccot ( \frac{t}{2} )}{18 0 ^{\circ}} + 3 n - \frac{1}{2}

y = \frac{3 arccot ( \frac{t}{2} )}{18 0 ^{\circ}} + 3 n - \frac{1}{2}

sec (y) = - 2

- 1 + 2 sin^{2} (x) = 0

θ, y = - 2 + cos (3 θ)

cos (2 x) + 5 \cdot cos (x) = - 3

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

What is the general solution for solvefor y,t=2cot(60y+30) ?
The general solution for solvefor y,t=2cot(60y+30) is y=(3arccot(t/2))/(180)+3n-1/2