What is the general solution for sin(x-53.13)=-2/5 ?

The general solution for sin(x-53.13)=-2/5 is x=-0.41151…+360n+53.13,x=180+0.41151…+360n+53.13

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sin(x-53.13)=-2/5

sin (x - 53.1 3^{\circ}) = - \frac{2}{5}

x = - 0.41151 \dots + 36 0^{\circ} n + 53.1 3^{\circ}, x = 18 0^{\circ} + 0.41151 \dots + 36 0^{\circ} n + 53.1 3^{\circ}

Radians

x = - 0.41151 \dots + \frac{1771 π}{6000} + 2 πn, x = π + 0.41151 \dots + \frac{1771 π}{6000} + 2 πn

Solution steps

sin (x - 53.1 3^{\circ}) = - \frac{2}{5}

Apply trig inverse properties

sin (x - 53.1 3^{\circ}) = - \frac{2}{5}

General solutions for

sin (x - 53.1 3^{\circ}) = - \frac{2}{5}

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

x - 53.1 3^{\circ} = arcsin (- \frac{2}{5}) + 36 0^{\circ} n, x - 53.1 3^{\circ} = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n

x - 53.1 3^{\circ} = arcsin (- \frac{2}{5}) + 36 0^{\circ} n, x - 53.1 3^{\circ} = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n

Solve

x - 53.1 3^{\circ} = arcsin (- \frac{2}{5}) + 36 0^{\circ} n : x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

x - 53.1 3^{\circ} = arcsin (- \frac{2}{5}) + 36 0^{\circ} n

Simplify

arcsin (- \frac{2}{5}) + 36 0^{\circ} n : - arcsin (\frac{2}{5}) + 36 0^{\circ} n

arcsin (- \frac{2}{5}) + 36 0^{\circ} n

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{5}) = - arcsin (\frac{2}{5})

= - arcsin (\frac{2}{5}) + 36 0^{\circ} n

x - 53.1 3^{\circ} = - arcsin (\frac{2}{5}) + 36 0^{\circ} n

Move

53.1 3^{\circ}

to the right side

x - 53.1 3^{\circ} = - arcsin (\frac{2}{5}) + 36 0^{\circ} n

Add

53.1 3^{\circ}

to both sides

x - 53.1 3^{\circ} + 53.1 3^{\circ} = - arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

Simplify

x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

Solve

x - 53.1 3^{\circ} = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n : x = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

x - 53.1 3^{\circ} = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n

Move

53.1 3^{\circ}

to the right side

x - 53.1 3^{\circ} = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n

Add

53.1 3^{\circ}

to both sides

x - 53.1 3^{\circ} + 53.1 3^{\circ} = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

Simplify

x = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

x = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}, x = 18 0^{\circ} + arcsin (\frac{2}{5}) + 36 0^{\circ} n + 53.1 3^{\circ}

Show solutions in decimal form

x = - 0.41151 \dots + 36 0^{\circ} n + 53.1 3^{\circ}, x = 18 0^{\circ} + 0.41151 \dots + 36 0^{\circ} n + 53.1 3^{\circ}

2 csc (x) + 2 = 0

1 + cos (x) = 3 cos (x)

cos (θ) = \frac{14}{16}

2 sec (x^{2}) + tan (x^{2}) - 3 = 0

5 + cos^{2} (θ) - 6 cos (θ) = 0

What is the general solution for sin(x-53.13)=-2/5 ?
The general solution for sin(x-53.13)=-2/5 is x=-0.41151…+360n+53.13,x=180+0.41151…+360n+53.13