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Popular >

sin(3θ-15)=0.7

Solution

sin (3 θ - 15) = 0.7

Solution

θ = 5 + \frac{2 πn}{3} + \frac{0.77539 \dots}{3}, θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{0.77539 \dots}{3} + 5

+1

Degrees

θ = 301.28789 \dots^{\circ} + 12 0^{\circ} n, θ = 331.66989 \dots^{\circ} + 12 0^{\circ} n

Solution steps

sin (3 θ - 15) = 0.7

Apply trig inverse properties

sin (3 θ - 15) = 0.7

General solutions for

sin (3 θ - 15) = 0.7

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

3 θ - 15 = arcsin (0.7) + 2 πn, 3 θ - 15 = π - arcsin (0.7) + 2 πn

3 θ - 15 = arcsin (0.7) + 2 πn, 3 θ - 15 = π - arcsin (0.7) + 2 πn

Solve

3 θ - 15 = arcsin (0.7) + 2 πn : θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

3 θ - 15 = arcsin (0.7) + 2 πn

Move

15

to the right side

3 θ - 15 = arcsin (0.7) + 2 πn

Add

15

to both sides

3 θ - 15 + 15 = arcsin (0.7) + 2 πn + 15

Simplify

3 θ = arcsin (0.7) + 2 πn + 15

3 θ = arcsin (0.7) + 2 πn + 15

Divide both sides by

3

3 θ = arcsin (0.7) + 2 πn + 15

Divide both sides by

3

\frac{3 θ}{3} = \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

Simplify

\frac{3 θ}{3} = \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3} : 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

\frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

Group like terms

= \frac{15}{3} + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

Divide the numbers:

\frac{15}{3} = 5

= 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

Solve

3 θ - 15 = π - arcsin (0.7) + 2 πn : θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

3 θ - 15 = π - arcsin (0.7) + 2 πn

Move

15

to the right side

3 θ - 15 = π - arcsin (0.7) + 2 πn

Add

15

to both sides

3 θ - 15 + 15 = π - arcsin (0.7) + 2 πn + 15

Simplify

3 θ = π - arcsin (0.7) + 2 πn + 15

3 θ = π - arcsin (0.7) + 2 πn + 15

Divide both sides by

3

3 θ = π - arcsin (0.7) + 2 πn + 15

Divide both sides by

3

\frac{3 θ}{3} = \frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

Simplify

\frac{3 θ}{3} = \frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3} : \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

\frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

Group like terms

= \frac{π}{3} + \frac{15}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3}

Divide the numbers:

\frac{15}{3} = 5

= \frac{π}{3} + 5 + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3}

Group like terms

= \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}, θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

Show solutions in decimal form

θ = 5 + \frac{2 πn}{3} + \frac{0.77539 \dots}{3}, θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{0.77539 \dots}{3} + 5

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