What is the general solution for 7sin(B)+3=sin(B)+2 ?

The general solution for 7sin(B)+3=sin(B)+2 is B=-0.16744…+2pin,B=pi+0.16744…+2pin

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7sin(B)+3=sin(B)+2

7 sin (B) + 3 = sin (B) + 2

B = - 0.16744 \dots + 2 πn, B = π + 0.16744 \dots + 2 πn

Solution steps

7 sin (B) + 3 = sin (B) + 2

Solve by substitution

sin (B) = - \frac{1}{6}

sin (B) = - \frac{1}{6} : B = arcsin (- \frac{1}{6}) + 2 πn, B = π + arcsin (\frac{1}{6}) + 2 πn

Combine all the solutions

B = arcsin (- \frac{1}{6}) + 2 πn, B = π + arcsin (\frac{1}{6}) + 2 πn

Show solutions in decimal form

B = - 0.16744 \dots + 2 πn, B = π + 0.16744 \dots + 2 πn

4 cos (x) = 3

cos (x + \frac{1}{6} π) cos (x - \frac{1}{6} π) = cos (2 x)

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

sin (x) = 0.731

sin (x) = 0.766

What is the general solution for 7sin(B)+3=sin(B)+2 ?
The general solution for 7sin(B)+3=sin(B)+2 is B=-0.16744…+2pin,B=pi+0.16744…+2pin