What is the general solution for 6sin(t)=3 ?

The general solution for 6sin(t)=3 is t= pi/6+2pin,t=(5pi)/6+2pin

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6sin(t)=3

6 sin (t) = 3

t = \frac{π}{6} + 2 πn, t = \frac{5 π}{6} + 2 πn

Degrees

t = 3 0^{\circ} + 36 0^{\circ} n, t = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

6 sin (t) = 3

Divide both sides by

6

6 sin (t) = 3

Divide both sides by

6

\frac{6 sin ( t )}{6} = \frac{3}{6}

Simplify

sin (t) = \frac{1}{2}

sin (t) = \frac{1}{2}

General solutions for

sin (t) = \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

t = \frac{π}{6} + 2 πn, t = \frac{5 π}{6} + 2 πn

t = \frac{π}{6} + 2 πn, t = \frac{5 π}{6} + 2 πn

arctan (e^{x}) = \frac{π}{4}

csc^{2} (x) + 2 cos (x) + 1 = 0

2 cos^{2} (2 x) + 3 cos (2 x) - 2 = 0

tan (t) = - \frac{12}{5}, \frac{3 π}{2} < t < 2 π

3 sin (x) + 5 cos (x) = 4

What is the general solution for 6sin(t)=3 ?
The general solution for 6sin(t)=3 is t= pi/6+2pin,t=(5pi)/6+2pin