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Popular >

35+53sin(2T-31.9)=0

Solution

35 + 53 sin (2 T - 31.9) = 0

Solution

T = πn + \frac{31.9}{2} - \frac{0.72132 \dots}{2}, T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{0.72132 \dots}{2}

+1

Degrees

T = 893.20335 \dots^{\circ} + 18 0^{\circ} n, T = 1024.53201 \dots^{\circ} + 18 0^{\circ} n

Solution steps

35 + 53 sin (2 T - 31.9) = 0

Move

35

to the right side

35 + 53 sin (2 T - 31.9) = 0

Subtract

35

from both sides

35 + 53 sin (2 T - 31.9) - 35 = 0 - 35

Simplify

53 sin (2 T - 31.9) = - 35

53 sin (2 T - 31.9) = - 35

Divide both sides by

53

53 sin (2 T - 31.9) = - 35

Divide both sides by

53

\frac{53 sin ( 2 T - 31.9 )}{53} = \frac{- 35}{53}

Simplify

sin (2 T - 31.9) = - \frac{35}{53}

sin (2 T - 31.9) = - \frac{35}{53}

Apply trig inverse properties

sin (2 T - 31.9) = - \frac{35}{53}

General solutions for

sin (2 T - 31.9) = - \frac{35}{53}

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

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn, 2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn, 2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

Solve

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn : T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn

Simplify

arcsin (- \frac{35}{53}) + 2 πn : - arcsin (\frac{35}{53}) + 2 πn

arcsin (- \frac{35}{53}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{35}{53}) = - arcsin (\frac{35}{53})

= - arcsin (\frac{35}{53}) + 2 πn

2 T - 31.9 = - arcsin (\frac{35}{53}) + 2 πn

Move

31.9

to the right side

2 T - 31.9 = - arcsin (\frac{35}{53}) + 2 πn

Add

31.9

to both sides

2 T - 31.9 + 31.9 = - arcsin (\frac{35}{53}) + 2 πn + 31.9

Simplify

2 T = - arcsin (\frac{35}{53}) + 2 πn + 31.9

2 T = - arcsin (\frac{35}{53}) + 2 πn + 31.9

Divide both sides by

2

2 T = - arcsin (\frac{35}{53}) + 2 πn + 31.9

Divide both sides by

2

\frac{2 T}{2} = - \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

Simplify

\frac{2 T}{2} = - \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

Simplify

\frac{2 T}{2} : T

\frac{2 T}{2}

Divide the numbers:

\frac{2}{2} = 1

= T

Simplify

- \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2} : πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

- \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

Group like terms

= \frac{31.9}{2} + \frac{2 πn}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{31.9}{2} + πn - \frac{arcsin ( \frac{35}{53} )}{2}

Group like terms

= πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

Solve

2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn : T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

Move

31.9

to the right side

2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

Add

31.9

to both sides

2 T - 31.9 + 31.9 = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

Simplify

2 T = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

2 T = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

Divide both sides by

2

2 T = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

Divide both sides by

2

\frac{2 T}{2} = \frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

Simplify

\frac{2 T}{2} = \frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

Simplify

\frac{2 T}{2} : T

\frac{2 T}{2}

Divide the numbers:

\frac{2}{2} = 1

= T

Simplify

\frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2} : πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

\frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

Group like terms

= \frac{π}{2} + \frac{31.9}{2} + \frac{2 πn}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{31.9}{2} + πn + \frac{arcsin ( \frac{35}{53} )}{2}

Group like terms

= πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}, T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

Show solutions in decimal form

T = πn + \frac{31.9}{2} - \frac{0.72132 \dots}{2}, T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{0.72132 \dots}{2}

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