What is the general solution for 5sin(a)+3=sin(a)+2 ?

The general solution for 5sin(a)+3=sin(a)+2 is a=-0.25268…+2pin,a=pi+0.25268…+2pin

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5sin(a)+3=sin(a)+2

5 sin (a) + 3 = sin (a) + 2

a = - 0.25268 \dots + 2 πn, a = π + 0.25268 \dots + 2 πn

Solution steps

5 sin (a) + 3 = sin (a) + 2

Solve by substitution

sin (a) = - \frac{1}{4}

sin (a) = - \frac{1}{4} : a = arcsin (- \frac{1}{4}) + 2 πn, a = π + arcsin (\frac{1}{4}) + 2 πn

Combine all the solutions

a = arcsin (- \frac{1}{4}) + 2 πn, a = π + arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

a = - 0.25268 \dots + 2 πn, a = π + 0.25268 \dots + 2 πn

csc (3 x) = 2

sin (x) = 0, 6

4 cos^{2} (θ) - 3 = 0, 0 \leq θ \leq 2 π

2 sin (θ) - 3 = - csc (θ)

cot (θ) = - 3

What is the general solution for 5sin(a)+3=sin(a)+2 ?
The general solution for 5sin(a)+3=sin(a)+2 is a=-0.25268…+2pin,a=pi+0.25268…+2pin