What is the general solution for -4sin(c)-2=sin(c)+1 ?

The general solution for -4sin(c)-2=sin(c)+1 is c=-0.64350…+2pin,c=pi+0.64350…+2pin

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Popular Trigonometry >

-4sin(c)-2=sin(c)+1

Solution

- 4 sin (c) - 2 = sin (c) + 1

Solution

c = - 0.64350 \dots + 2 πn, c = π + 0.64350 \dots + 2 πn

Degrees

c = - 36.86989 \dots^{\circ} + 36 0^{\circ} n, c = 216.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 4 sin (c) - 2 = sin (c) + 1

Solve by substitution

- 4 sin (c) - 2 = sin (c) + 1

Let:

sin (c) = u

- 4 u - 2 = u + 1

- 4 u - 2 = u + 1 : u = - \frac{3}{5}

- 4 u - 2 = u + 1

Move

2

to the right side

- 4 u - 2 = u + 1

Add

2

to both sides

- 4 u - 2 + 2 = u + 1 + 2

Simplify

- 4 u = u + 3

- 4 u = u + 3

Move

u

to the left side

- 4 u = u + 3

Subtract

u

from both sides

- 4 u - u = u + 3 - u

Simplify

- 5 u = 3

- 5 u = 3

Divide both sides by

- 5

- 5 u = 3

Divide both sides by

- 5

\frac{- 5 u}{- 5} = \frac{3}{- 5}

Simplify

u = - \frac{3}{5}

u = - \frac{3}{5}

Substitute back

u = sin (c)

sin (c) = - \frac{3}{5}

sin (c) = - \frac{3}{5}

sin (c) = - \frac{3}{5} : c = arcsin (- \frac{3}{5}) + 2 πn, c = π + arcsin (\frac{3}{5}) + 2 πn

sin (c) = - \frac{3}{5}

Apply trig inverse properties

sin (c) = - \frac{3}{5}

General solutions for

sin (c) = - \frac{3}{5}

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

c = arcsin (- \frac{3}{5}) + 2 πn, c = π + arcsin (\frac{3}{5}) + 2 πn

c = arcsin (- \frac{3}{5}) + 2 πn, c = π + arcsin (\frac{3}{5}) + 2 πn

Combine all the solutions

c = arcsin (- \frac{3}{5}) + 2 πn, c = π + arcsin (\frac{3}{5}) + 2 πn

Show solutions in decimal form

c = - 0.64350 \dots + 2 πn, c = π + 0.64350 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for -4sin(c)-2=sin(c)+1 ?
The general solution for -4sin(c)-2=sin(c)+1 is c=-0.64350…+2pin,c=pi+0.64350…+2pin