What is the general solution for 8.5=12sin(a) ?

The general solution for 8.5=12sin(a) is a=0.78713…+2pin,a=pi-0.78713…+2pin

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8.5=12sin(a)

8.5 = 12 sin (a)

a = 0.78713 \dots + 2 πn, a = π - 0.78713 \dots + 2 πn

Degrees

a = 45.09947 \dots^{\circ} + 36 0^{\circ} n, a = 134.90052 \dots^{\circ} + 36 0^{\circ} n

Solution steps

8.5 = 12 sin (a)

Switch sides

12 sin (a) = 8.5

Divide both sides by

12

12 sin (a) = 8.5

Divide both sides by

12

\frac{12 sin ( a )}{12} = \frac{8.5}{12}

Simplify

sin (a) = 0.70833 \dots

sin (a) = 0.70833 \dots

Apply trig inverse properties

sin (a) = 0.70833 \dots

General solutions for

sin (a) = 0.70833 \dots

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

a = arcsin (0.70833 \dots) + 2 πn, a = π - arcsin (0.70833 \dots) + 2 πn

a = arcsin (0.70833 \dots) + 2 πn, a = π - arcsin (0.70833 \dots) + 2 πn

Show solutions in decimal form

a = 0.78713 \dots + 2 πn, a = π - 0.78713 \dots + 2 πn

cos (x) = \frac{1}{15}

cot (θ) = - 3, 0 \leq θ < 2 π

\frac{sin ( 9 0 ^{\circ} )}{458.912} = \frac{sin ( x )}{450}

0 = \frac{2 π ^{2} cos ( \frac{π x}{10} )}{25}

300 cos (7 0^{\circ}) = 375 cos (θ)

What is the general solution for 8.5=12sin(a) ?
The general solution for 8.5=12sin(a) is a=0.78713…+2pin,a=pi-0.78713…+2pin