What is the general solution for 4sin(x)+5=4+sin(x) ?

The general solution for 4sin(x)+5=4+sin(x) is x=-0.33983…+2pin,x=pi+0.33983…+2pin

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4sin(x)+5=4+sin(x)

4 sin (x) + 5 = 4 + sin (x)

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

Solution steps

4 sin (x) + 5 = 4 + sin (x)

Solve by substitution

sin (x) = - \frac{1}{3}

sin (x) = - \frac{1}{3} : x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

Combine all the solutions

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

9 sin (θ) - 1 = 7 sin (θ)

cot (x) = sin (x)

- 3 cos (x) - sin (x) = - 3

9 cot^{2} (x) = 3

cos (x) = - 2

What is the general solution for 4sin(x)+5=4+sin(x) ?
The general solution for 4sin(x)+5=4+sin(x) is x=-0.33983…+2pin,x=pi+0.33983…+2pin