What is the general solution for sin(x+60)=-0.4 ?

The general solution for sin(x+60)=-0.4 is x=-0.41151…+360n-60,x=180+0.41151…+360n-60

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sin(x+60)=-0.4

sin (x + 6 0^{\circ}) = - 0.4

x = - 0.41151 \dots + 36 0^{\circ} n - 6 0^{\circ}, x = 18 0^{\circ} + 0.41151 \dots + 36 0^{\circ} n - 6 0^{\circ}

Radians

x = - 0.41151 \dots - \frac{π}{3} + 2 πn, x = π + 0.41151 \dots - \frac{π}{3} + 2 πn

Solution steps

sin (x + 6 0^{\circ}) = - 0.4

Apply trig inverse properties

sin (x + 6 0^{\circ}) = - 0.4

General solutions for

sin (x + 6 0^{\circ}) = - 0.4

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

x + 6 0^{\circ} = arcsin (- 0.4) + 36 0^{\circ} n, x + 6 0^{\circ} = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n

x + 6 0^{\circ} = arcsin (- 0.4) + 36 0^{\circ} n, x + 6 0^{\circ} = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n

Solve

x + 6 0^{\circ} = arcsin (- 0.4) + 36 0^{\circ} n : x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n - 6 0^{\circ}

x + 6 0^{\circ} = arcsin (- 0.4) + 36 0^{\circ} n

Simplify

arcsin (- 0.4) + 36 0^{\circ} n : - arcsin (\frac{2}{5}) + 36 0^{\circ} n

arcsin (- 0.4) + 36 0^{\circ} n

arcsin (- 0.4) = - arcsin (\frac{2}{5})

arcsin (- 0.4)

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

Use the following property:

arcsin (- x) = - arcsin (x)

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

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

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

x + 6 0^{\circ} = - arcsin (\frac{2}{5}) + 36 0^{\circ} n

Move

6 0^{\circ}

to the right side

x + 6 0^{\circ} = - arcsin (\frac{2}{5}) + 36 0^{\circ} n

Subtract

6 0^{\circ}

from both sides

x + 6 0^{\circ} - 6 0^{\circ} = - arcsin (\frac{2}{5}) + 36 0^{\circ} n - 6 0^{\circ}

Simplify

x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n - 6 0^{\circ}

x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n - 6 0^{\circ}

Solve

x + 6 0^{\circ} = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n : x = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n - 6 0^{\circ}

x + 6 0^{\circ} = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n

Move

6 0^{\circ}

to the right side

x + 6 0^{\circ} = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n

Subtract

6 0^{\circ}

from both sides

x + 6 0^{\circ} - 6 0^{\circ} = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n - 6 0^{\circ}

Simplify

x = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n - 6 0^{\circ}

x = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n - 6 0^{\circ}

x = - arcsin (\frac{2}{5}) + 36 0^{\circ} n - 6 0^{\circ}, x = 18 0^{\circ} + arcsin (0.4) + 36 0^{\circ} n - 6 0^{\circ}

Show solutions in decimal form

x = - 0.41151 \dots + 36 0^{\circ} n - 6 0^{\circ}, x = 18 0^{\circ} + 0.41151 \dots + 36 0^{\circ} n - 6 0^{\circ}

1 = sin (2 x)

- 0.15 = cos (θ)

cos (x) = 90

tan (x) = \frac{14}{29}

sin (x) + sin (2 x) - sin (3 x) = 0

What is the general solution for sin(x+60)=-0.4 ?
The general solution for sin(x+60)=-0.4 is x=-0.41151…+360n-60,x=180+0.41151…+360n-60