What is the general solution for pi/6 =cos(2t) ?

The general solution for pi/6 =cos(2t) is t=(1.01972…)/2+pin,t=pi-(1.01972…)/2+pin

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pi/6 =cos(2t)

\frac{π}{6} = cos (2 t)

t = \frac{1.01972 \dots}{2} + πn, t = π - \frac{1.01972 \dots}{2} + πn

Degrees

t = 29.21301 \dots^{\circ} + 18 0^{\circ} n, t = 150.78698 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{π}{6} = cos (2 t)

Switch sides

cos (2 t) = \frac{π}{6}

Apply trig inverse properties

cos (2 t) = \frac{π}{6}

General solutions for

cos (2 t) = \frac{π}{6}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

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

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

Solve

2 t = arccos (\frac{π}{6}) + 2 πn : t = \frac{arccos ( \frac{π}{6} )}{2} + πn

2 t = arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

2 t = arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

\frac{2 t}{2} = \frac{arccos ( \frac{π}{6} )}{2} + \frac{2 πn}{2}

Simplify

t = \frac{arccos ( \frac{π}{6} )}{2} + πn

t = \frac{arccos ( \frac{π}{6} )}{2} + πn

Solve

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

2 t = 2 π - arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

2 t = 2 π - arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

\frac{2 t}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{π}{6} )}{2} + \frac{2 πn}{2}

Simplify

t = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

t = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

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

Show solutions in decimal form

t = \frac{1.01972 \dots}{2} + πn, t = π - \frac{1.01972 \dots}{2} + πn

x, 3 tan (2 x) = 1

y, x = 5 \cdot sin (y)

12 cos^{2} (x) - cos (x) - 1 = 0

t, x = a cos^{2} (t) + b sin^{2} (t)

cos (3 x) - sin (3 x) = 0

What is the general solution for pi/6 =cos(2t) ?
The general solution for pi/6 =cos(2t) is t=(1.01972…)/2+pin,t=pi-(1.01972…)/2+pin