What is the general solution for 10sin(x)+1=3-2sin(x) ?

The general solution for 10sin(x)+1=3-2sin(x) is x=0.16744…+2pin,x=pi-0.16744…+2pin

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10sin(x)+1=3-2sin(x)

10 sin (x) + 1 = 3 - 2 sin (x)

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

Solution steps

10 sin (x) + 1 = 3 - 2 sin (x)

Solve by substitution

sin (x) = \frac{1}{6}

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

Combine all the solutions

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

Show solutions in decimal form

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

2 cos (x) - 9 = - 4 sec (x)

2 sin (θ) + 4 = 4

4 sin^{2} (x) + (23 + 2) sin (x) + 3 = 0

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

3 csc (x) = 2 csc (x) + 2

What is the general solution for 10sin(x)+1=3-2sin(x) ?
The general solution for 10sin(x)+1=3-2sin(x) is x=0.16744…+2pin,x=pi-0.16744…+2pin