What is the general solution for 2sin(x+1.2)-4.22=-4 ?

The general solution for 2sin(x+1.2)-4.22=-4 is x=0.11022…+2pin-1.2,x=pi-0.11022…+2pin-1.2

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Popular >

2sin(x+1.2)-4.22=-4

Solution

2 sin (x + 1.2) - 4.22 = - 4

Solution

x = 0.11022 \dots + 2 πn - 1.2, x = π - 0.11022 \dots + 2 πn - 1.2

Degrees

x = - 62.43961 \dots^{\circ} + 36 0^{\circ} n, x = 104.92974 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 sin (x + 1.2) - 4.22 = - 4

Move

4.22

to the right side

2 sin (x + 1.2) - 4.22 = - 4

Add

4.22

to both sides

2 sin (x + 1.2) - 4.22 + 4.22 = - 4 + 4.22

Simplify

2 sin (x + 1.2) = 0.22

2 sin (x + 1.2) = 0.22

Divide both sides by

2

2 sin (x + 1.2) = 0.22

Divide both sides by

2

\frac{2 sin ( x + 1.2 )}{2} = \frac{0.22}{2}

Simplify

sin (x + 1.2) = 0.11

sin (x + 1.2) = 0.11

Apply trig inverse properties

sin (x + 1.2) = 0.11

General solutions for

sin (x + 1.2) = 0.11

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

x + 1.2 = arcsin (0.11) + 2 πn, x + 1.2 = π - arcsin (0.11) + 2 πn

x + 1.2 = arcsin (0.11) + 2 πn, x + 1.2 = π - arcsin (0.11) + 2 πn

Solve

x + 1.2 = arcsin (0.11) + 2 πn : x = arcsin (0.11) + 2 πn - 1.2

x + 1.2 = arcsin (0.11) + 2 πn

Move

1.2

to the right side

x + 1.2 = arcsin (0.11) + 2 πn

Subtract

1.2

from both sides

x + 1.2 - 1.2 = arcsin (0.11) + 2 πn - 1.2

Simplify

x = arcsin (0.11) + 2 πn - 1.2

x = arcsin (0.11) + 2 πn - 1.2

Solve

x + 1.2 = π - arcsin (0.11) + 2 πn : x = π - arcsin (0.11) + 2 πn - 1.2

x + 1.2 = π - arcsin (0.11) + 2 πn

Move

1.2

to the right side

x + 1.2 = π - arcsin (0.11) + 2 πn

Subtract

1.2

from both sides

x + 1.2 - 1.2 = π - arcsin (0.11) + 2 πn - 1.2

Simplify

x = π - arcsin (0.11) + 2 πn - 1.2

x = π - arcsin (0.11) + 2 πn - 1.2

x = arcsin (0.11) + 2 πn - 1.2, x = π - arcsin (0.11) + 2 πn - 1.2

Show solutions in decimal form

x = 0.11022 \dots + 2 πn - 1.2, x = π - 0.11022 \dots + 2 πn - 1.2

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Frequently Asked Questions (FAQ)

What is the general solution for 2sin(x+1.2)-4.22=-4 ?
The general solution for 2sin(x+1.2)-4.22=-4 is x=0.11022…+2pin-1.2,x=pi-0.11022…+2pin-1.2