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Popular Trigonometry >

((0.871.04sin(20-x))/(0.4))=0.05

Solution

(\frac{0.87 \cdot 1.04 \cdot sin ( 2 0 ^{\circ} - x )}{0.4}) = 0.05

Solution

x = - 36 0^{\circ} n + 2 0^{\circ} - 0.02210 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + 0.02210 \dots

Radians

x = \frac{π}{9} - 0.02210 \dots - 2 πn, x = - π + \frac{π}{9} + 0.02210 \dots - 2 πn

Solution steps

(\frac{0.87 \cdot 1.04 sin ( 2 0 ^{\circ} - x )}{0.4}) = 0.05

Multiply both sides by

0.4

\frac{0.87 \cdot 1.04 sin ( 2 0 ^{\circ} - x )}{0.4} = 0.05

Multiply both sides by

0.4

\frac{0.4 \cdot 0.87 \cdot 1.04 sin ( 2 0 ^{\circ} - x )}{0.4} = 0.05 \cdot 0.4

Simplify

0.9048 sin (2 0^{\circ} - x) = 0.02

0.9048 sin (2 0^{\circ} - x) = 0.02

Divide both sides by

0.9048

0.9048 sin (2 0^{\circ} - x) = 0.02

Divide both sides by

0.9048

\frac{0.9048 sin ( 2 0 ^{\circ} - x )}{0.9048} = \frac{0.02}{0.9048}

Simplify

sin (2 0^{\circ} - x) = 0.02210 \dots

sin (2 0^{\circ} - x) = 0.02210 \dots

Apply trig inverse properties

sin (2 0^{\circ} - x) = 0.02210 \dots

General solutions for

sin (2 0^{\circ} - x) = 0.02210 \dots

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

2 0^{\circ} - x = arcsin (0.02210 \dots) + 36 0^{\circ} n, 2 0^{\circ} - x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n

2 0^{\circ} - x = arcsin (0.02210 \dots) + 36 0^{\circ} n, 2 0^{\circ} - x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n

Solve

2 0^{\circ} - x = arcsin (0.02210 \dots) + 36 0^{\circ} n : x = - 36 0^{\circ} n + 2 0^{\circ} - arcsin (0.02210 \dots)

2 0^{\circ} - x = arcsin (0.02210 \dots) + 36 0^{\circ} n

Move

2 0^{\circ}

to the right side

2 0^{\circ} - x = arcsin (0.02210 \dots) + 36 0^{\circ} n

Subtract

2 0^{\circ}

from both sides

2 0^{\circ} - x - 2 0^{\circ} = arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

Simplify

- x = arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

- x = arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

- 1

- x = arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1}

Simplify

\frac{- x}{- 1} = \frac{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 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{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 2 0^{\circ} - arcsin (0.02210 \dots)

\frac{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1}

Group like terms

= \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1} + \frac{arcsin ( 0.02210 \dots )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Apply the fraction rule:

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

= - \frac{36 0 ^{\circ} n}{1}

Apply rule

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{2 0 ^{\circ}}{- 1} + \frac{arcsin ( 0.02210 \dots )}{- 1}

\frac{2 0 ^{\circ}}{- 1} = - 2 0^{\circ}

\frac{2 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - \frac{2 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{2 0 ^{\circ}}{1} = 2 0^{\circ}

= - 2 0^{\circ}

\frac{arcsin ( 0.02210 \dots )}{- 1} = - arcsin (0.02210 \dots)

\frac{arcsin ( 0.02210 \dots )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.02210 \dots )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.02210 \dots)

= - 36 0^{\circ} n - (- 2 0^{\circ}) - arcsin (0.02210 \dots)

Apply rule

- (- a) = a

= - 36 0^{\circ} n + 2 0^{\circ} - arcsin (0.02210 \dots)

x = - 36 0^{\circ} n + 2 0^{\circ} - arcsin (0.02210 \dots)

x = - 36 0^{\circ} n + 2 0^{\circ} - arcsin (0.02210 \dots)

x = - 36 0^{\circ} n + 2 0^{\circ} - arcsin (0.02210 \dots)

Solve

2 0^{\circ} - x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n : x = - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + arcsin (0.02210 \dots)

2 0^{\circ} - x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n

Move

2 0^{\circ}

to the right side

2 0^{\circ} - x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n

Subtract

2 0^{\circ}

from both sides

2 0^{\circ} - x - 2 0^{\circ} = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

Simplify

- x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

- x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

- 1

- x = 18 0^{\circ} - arcsin (0.02210 \dots) + 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1}

Simplify

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 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{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + arcsin (0.02210 \dots)

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.02210 \dots )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1}

Group like terms

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.02210 \dots )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - 18 0^{\circ}

Apply rule

\frac{a}{1} = a

= - 18 0^{\circ}

= - 18 0^{\circ} + \frac{36 0 ^{\circ} n}{- 1} - \frac{2 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.02210 \dots )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Apply the fraction rule:

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

= - \frac{36 0 ^{\circ} n}{1}

Apply rule

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 18 0^{\circ} - 36 0^{\circ} n - \frac{2 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.02210 \dots )}{- 1}

\frac{2 0 ^{\circ}}{- 1} = - 2 0^{\circ}

\frac{2 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - \frac{2 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{2 0 ^{\circ}}{1} = 2 0^{\circ}

= - 2 0^{\circ}

\frac{arcsin ( 0.02210 \dots )}{- 1} = - arcsin (0.02210 \dots)

\frac{arcsin ( 0.02210 \dots )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.02210 \dots )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.02210 \dots)

= - 18 0^{\circ} - 36 0^{\circ} n - (- 2 0^{\circ}) - (- arcsin (0.02210 \dots))

Apply rule

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + arcsin (0.02210 \dots)

x = - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + arcsin (0.02210 \dots)

x = - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + arcsin (0.02210 \dots)

x = - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + arcsin (0.02210 \dots)

x = - 36 0^{\circ} n + 2 0^{\circ} - arcsin (0.02210 \dots), x = - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + arcsin (0.02210 \dots)

Show solutions in decimal form

x = - 36 0^{\circ} n + 2 0^{\circ} - 0.02210 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 2 0^{\circ} + 0.02210 \dots

Graph

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((0.87*1.04*sin(20-x))/(0.4))=0.05

Solution

Solution

Graph

Popular Examples

((0.871.04sin(20-x))/(0.4))=0.05