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Popular Trigonometry >

950sin(pi/6 (7-x))+1650=2500

Solution

950 sin (\frac{π}{6} (7 - x)) + 1650 = 2500

Solution

x = 7 - 12 n - \frac{6 \cdot 1.10784 \dots}{π}, x = - 12 n + 1 + \frac{6 \cdot 1.10784 \dots}{π}

Degrees

x = 279.84280 \dots^{\circ} - 687.54935 \dots^{\circ} n, x = 178.52342 \dots^{\circ} - 687.54935 \dots^{\circ} n

Solution steps

950 sin (\frac{π}{6} (7 - x)) + 1650 = 2500

Move

1650

to the right side

950 sin (\frac{π}{6} (7 - x)) + 1650 = 2500

Subtract

1650

from both sides

950 sin (\frac{π}{6} (7 - x)) + 1650 - 1650 = 2500 - 1650

Simplify

950 sin (\frac{π}{6} (7 - x)) = 850

950 sin (\frac{π}{6} (7 - x)) = 850

Divide both sides by

950

950 sin (\frac{π}{6} (7 - x)) = 850

Divide both sides by

950

\frac{950 sin ( \frac{π}{6} ( 7 - x ) )}{950} = \frac{850}{950}

Simplify

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

Apply trig inverse properties

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

General solutions for

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

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

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn, \frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn, \frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

Solve

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn : x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn

Multiply both sides by

6

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn

Multiply both sides by

6

6 \cdot \frac{π}{6} (7 - x) = 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (7 - x) = 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (7 - x) : π (7 - x)

6 \cdot \frac{π}{6} (7 - x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 π}{6} (- x + 7)

Cancel the common factor:

6

= (7 - x) π

Simplify

6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn : 6 arcsin (\frac{17}{19}) + 12 πn

6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

Divide both sides by

π

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

Divide both sides by

π

\frac{π ( 7 - x )}{π} = \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Simplify

7 - x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Move

7

to the right side

7 - x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Subtract

7

from both sides

7 - x - 7 = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Simplify

- x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

- x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Divide both sides by

- 1

- x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1}

Simplify

\frac{- x}{- 1} = \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1} : 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1}

Group like terms

= - \frac{7}{- 1} + \frac{12 n}{- 1} + \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{7}{- 1} = - 7

\frac{7}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{7}{1}

Apply rule

\frac{a}{1} = a

= - 7

\frac{12 n}{- 1} = - 12 n

\frac{12 n}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{12 n}{1}

Apply rule

\frac{a}{1} = a

= - 12 n

= - (- 7) - 12 n + \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Apply rule

- (- a) = a

= 7 - 12 n + \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} = - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1} = \frac{6 arcsin ( \frac{17}{19} )}{π}

= - \frac{6 arcsin ( \frac{17}{19} )}{π}

= 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

Solve

\frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn : x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

Multiply both sides by

6

\frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

Multiply both sides by

6

6 \cdot \frac{π}{6} (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (7 - x) : π (7 - x)

6 \cdot \frac{π}{6} (7 - x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 π}{6} (- x + 7)

Cancel the common factor:

6

= (7 - x) π

Simplify

6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn : 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

Divide both sides by

π

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

Divide both sides by

π

\frac{π ( 7 - x )}{π} = \frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( 7 - x )}{π} = \frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( 7 - x )}{π} : 7 - x

\frac{π ( 7 - x )}{π}

Cancel the common factor:

π

= 7 - x

Simplify

\frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π} : 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

\frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Cancel

\frac{6 π}{π} : 6

\frac{6 π}{π}

Cancel the common factor:

π

= 6

= 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Cancel

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Cancel the common factor:

π

= 12 n

= 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Move

7

to the right side

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Subtract

7

from both sides

7 - x - 7 = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Simplify

7 - x - 7 = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Simplify

7 - x - 7 : - x

7 - x - 7

Add similar elements:

7 - 7 = 0

= - x

Simplify

6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7 : 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Subtract the numbers:

6 - 7 = - 1

= 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

Divide both sides by

- 1

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Simplify

\frac{- x}{- 1} = \frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} : - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{12 n}{- 1} = - 12 n

\frac{12 n}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{12 n}{1}

Apply rule

\frac{a}{1} = a

= - 12 n

= - 12 n - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{1}{- 1} = - 1

\frac{1}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{1}

Apply rule

\frac{a}{1} = a

= - 1

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} = - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1} = \frac{6 arcsin ( \frac{17}{19} )}{π}

= - \frac{6 arcsin ( \frac{17}{19} )}{π}

= - 12 n - (- 1) - (- \frac{6 arcsin ( \frac{17}{19} )}{π})

Apply rule

- (- a) = a

= - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}, x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

Show solutions in decimal form

x = 7 - 12 n - \frac{6 \cdot 1.10784 \dots}{π}, x = - 12 n + 1 + \frac{6 \cdot 1.10784 \dots}{π}

Graph

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