What is the general solution for -6sin(c)+0=sin(c)-3 ?

The general solution for -6sin(c)+0=sin(c)-3 is c=0.44291…+2pin,c=pi-0.44291…+2pin

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-6sin(c)+0=sin(c)-3

- 6 sin (c) + 0 = sin (c) - 3

c = 0.44291 \dots + 2 πn, c = π - 0.44291 \dots + 2 πn

Degrees

c = 25.37693 \dots^{\circ} + 36 0^{\circ} n, c = 154.62306 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 6 sin (c) + 0 = sin (c) - 3

Solve by substitution

- 6 sin (c) + 0 = sin (c) - 3

Let:

sin (c) = u

- 6 u + 0 = u - 3

- 6 u + 0 = u - 3 : u = \frac{3}{7}

- 6 u + 0 = u - 3

- 6 u + 0 = - 6 u

- 6 u = u - 3

Move

u

to the left side

- 6 u = u - 3

Subtract

u

from both sides

- 6 u - u = u - 3 - u

Simplify

- 7 u = - 3

- 7 u = - 3

Divide both sides by

- 7

- 7 u = - 3

Divide both sides by

- 7

\frac{- 7 u}{- 7} = \frac{- 3}{- 7}

Simplify

u = \frac{3}{7}

u = \frac{3}{7}

Substitute back

u = sin (c)

sin (c) = \frac{3}{7}

sin (c) = \frac{3}{7}

sin (c) = \frac{3}{7} : c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

sin (c) = \frac{3}{7}

Apply trig inverse properties

sin (c) = \frac{3}{7}

General solutions for

sin (c) = \frac{3}{7}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

Combine all the solutions

c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

Show solutions in decimal form

c = 0.44291 \dots + 2 πn, c = π - 0.44291 \dots + 2 πn

tan (x) = \frac{11}{12}

2 cos (a) + 3 = 4

tan (x) cot (x) - 3 tan (x) = 0

cos (θ) = 0.139

- \frac{2 3}{3} = sec (θ)

What is the general solution for -6sin(c)+0=sin(c)-3 ?
The general solution for -6sin(c)+0=sin(c)-3 is c=0.44291…+2pin,c=pi-0.44291…+2pin