What is the general solution for 5=10sin(a) ?

The general solution for 5=10sin(a) is a= pi/6+2pin,a=(5pi)/6+2pin

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5=10sin(a)

5 = 10 sin (a)

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

Degrees

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

Solution steps

5 = 10 sin (a)

Switch sides

10 sin (a) = 5

Divide both sides by

10

10 sin (a) = 5

Divide both sides by

10

\frac{10 sin ( a )}{10} = \frac{5}{10}

Simplify

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

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

General solutions for

sin (a) = \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}

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

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

sin (θ) = cos (2 θ + 5 4^{\circ})

t, y = cos (t)

x, r^{2} = 9 cos (2 x)

csc (a) = \frac{13}{12}

(cos (θ) + 1) (tan (θ) + 1) = 0

What is the general solution for 5=10sin(a) ?
The general solution for 5=10sin(a) is a= pi/6+2pin,a=(5pi)/6+2pin