What is the general solution for sin(b)=12((sin(42))/(22)) ?

The general solution for sin(b)=12((sin(42))/(22)) is b=0.37361…+360n,b=180-0.37361…+360n

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sin(b)=12((sin(42))/(22))

sin (b) = 12 (\frac{sin ( 4 2 ^{\circ} )}{22})

b = 0.37361 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.37361 \dots + 36 0^{\circ} n

Solution steps

sin (b) = 12 (\frac{sin ( 4 2 ^{\circ} )}{22})

Simplify

12 \cdot \frac{sin ( 4 2 ^{\circ} )}{22} : \frac{6 sin ( 4 2 ^{\circ} )}{11}

Apply trig inverse properties

b = arcsin (\frac{6 sin ( 4 2 ^{\circ} )}{11}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{6 sin ( 4 2 ^{\circ} )}{11}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.37361 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.37361 \dots + 36 0^{\circ} n

arctan (\frac{3}{1}) = tan (θ)

2 sin^{2} (x) - 5 cos (x) + 5 = 0

tan (x) = \frac{20}{40}

2 sin (x + \frac{π}{4}) = 0

sin (x) = \frac{2 ( 5.5 \cdot 1 0 ^{- 7} )}{3.36 \cdot 1 0 ^{- 5}}

What is the general solution for sin(b)=12((sin(42))/(22)) ?
The general solution for sin(b)=12((sin(42))/(22)) is b=0.37361…+360n,b=180-0.37361…+360n