What is the general solution for 10sin(x)+16=3sin(x)+9 ?

The general solution for 10sin(x)+16=3sin(x)+9 is x=(3pi)/2+2pin

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10sin(x)+16=3sin(x)+9

10 sin (x) + 16 = 3 sin (x) + 9

x = \frac{3 π}{2} + 2 πn

Degrees

x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

10 sin (x) + 16 = 3 sin (x) + 9

Solve by substitution

10 sin (x) + 16 = 3 sin (x) + 9

Let:

sin (x) = u

10 u + 16 = 3 u + 9

10 u + 16 = 3 u + 9 : u = - 1

10 u + 16 = 3 u + 9

Move

16

to the right side

10 u + 16 = 3 u + 9

Subtract

16

from both sides

10 u + 16 - 16 = 3 u + 9 - 16

Simplify

10 u = 3 u - 7

10 u = 3 u - 7

Move

3 u

to the left side

10 u = 3 u - 7

Subtract

3 u

from both sides

10 u - 3 u = 3 u - 7 - 3 u

Simplify

7 u = - 7

7 u = - 7

Divide both sides by

7

7 u = - 7

Divide both sides by

7

\frac{7 u}{7} = \frac{- 7}{7}

Simplify

u = - 1

u = - 1

Substitute back

u = sin (x)

sin (x) = - 1

sin (x) = - 1

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

sin (x) = - 1

General solutions for

sin (x) = - 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

2 sin (5 θ) = 0

x, sin^{2} (x) = 1

tan^{4} (x) - 2 = tan^{2} (x) + sec^{2} (x)

cos (x - \frac{π}{4}) = - sin (x)

sin (x) = \frac{5}{13}, cos (x)

What is the general solution for 10sin(x)+16=3sin(x)+9 ?
The general solution for 10sin(x)+16=3sin(x)+9 is x=(3pi)/2+2pin