What is the general solution for 4sin(x-30)-1.3=0 ?

The general solution for 4sin(x-30)-1.3=0 is x=0.33101…+360n+30,x=180-0.33101…+360n+30

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Popular >

4sin(x-30)-1.3=0

Solution

4 sin (x - 3 0^{\circ}) - 1.3 = 0

Solution

x = 0.33101 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 0.33101 \dots + 36 0^{\circ} n + 3 0^{\circ}

Radians

x = 0.33101 \dots + \frac{π}{6} + 2 πn, x = π - 0.33101 \dots + \frac{π}{6} + 2 πn

Solution steps

4 sin (x - 3 0^{\circ}) - 1.3 = 0

Move

1.3

to the right side

4 sin (x - 3 0^{\circ}) - 1.3 = 0

Add

1.3

to both sides

4 sin (x - 3 0^{\circ}) - 1.3 + 1.3 = 0 + 1.3

Simplify

4 sin (x - 3 0^{\circ}) = 1.3

4 sin (x - 3 0^{\circ}) = 1.3

Divide both sides by

4

4 sin (x - 3 0^{\circ}) = 1.3

Divide both sides by

4

\frac{4 sin ( x - 3 0 ^{\circ} )}{4} = \frac{1.3}{4}

Simplify

sin (x - 3 0^{\circ}) = 0.325

sin (x - 3 0^{\circ}) = 0.325

Apply trig inverse properties

sin (x - 3 0^{\circ}) = 0.325

General solutions for

sin (x - 3 0^{\circ}) = 0.325

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x - 3 0^{\circ} = arcsin (0.325) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n

x - 3 0^{\circ} = arcsin (0.325) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n

Solve

x - 3 0^{\circ} = arcsin (0.325) + 36 0^{\circ} n : x = arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = arcsin (0.325) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = arcsin (0.325) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

Solve

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - arcsin (0.325) + 36 0^{\circ} n + 3 0^{\circ}

Show solutions in decimal form

x = 0.33101 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 0.33101 \dots + 36 0^{\circ} n + 3 0^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for 4sin(x-30)-1.3=0 ?
The general solution for 4sin(x-30)-1.3=0 is x=0.33101…+360n+30,x=180-0.33101…+360n+30