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

The general solution for -sin(A)-1=3sin(A)+2 is A=-0.84806…+2pin,A=pi+0.84806…+2pin

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-sin(A)-1=3sin(A)+2

- sin (A) - 1 = 3 sin (A) + 2

A = - 0.84806 \dots + 2 πn, A = π + 0.84806 \dots + 2 πn

Solution steps

- sin (A) - 1 = 3 sin (A) + 2

Solve by substitution

sin (A) = - \frac{3}{4}

sin (A) = - \frac{3}{4} : A = arcsin (- \frac{3}{4}) + 2 πn, A = π + arcsin (\frac{3}{4}) + 2 πn

Combine all the solutions

A = arcsin (- \frac{3}{4}) + 2 πn, A = π + arcsin (\frac{3}{4}) + 2 πn

Show solutions in decimal form

A = - 0.84806 \dots + 2 πn, A = π + 0.84806 \dots + 2 πn

2 + cos (2 x) = 3 cos (x)

3 cot (θ) + 4 = 0

2 sin (3 θ) = 0

cot (t) = 3

3 sin (2 x) = 2

What is the general solution for -sin(A)-1=3sin(A)+2 ?
The general solution for -sin(A)-1=3sin(A)+2 is A=-0.84806…+2pin,A=pi+0.84806…+2pin