What is the general solution for sin(60-a)=0.598 ?

The general solution for sin(60-a)=0.598 is a=-360n+60-0.64100…,a=-180-360n+60+0.64100…

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Popular >

sin(60-a)=0.598

Solution

sin (6 0^{\circ} - a) = 0.598

Solution

a = - 36 0^{\circ} n + 6 0^{\circ} - 0.64100 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + 0.64100 \dots

Radians

a = \frac{π}{3} - 0.64100 \dots - 2 πn, a = - π + \frac{π}{3} + 0.64100 \dots - 2 πn

Solution steps

sin (6 0^{\circ} - a) = 0.598

Apply trig inverse properties

sin (6 0^{\circ} - a) = 0.598

General solutions for

sin (6 0^{\circ} - a) = 0.598

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

6 0^{\circ} - a = arcsin (0.598) + 36 0^{\circ} n, 6 0^{\circ} - a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n

6 0^{\circ} - a = arcsin (0.598) + 36 0^{\circ} n, 6 0^{\circ} - a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n

Solve

6 0^{\circ} - a = arcsin (0.598) + 36 0^{\circ} n : a = - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598)

6 0^{\circ} - a = arcsin (0.598) + 36 0^{\circ} n

Move

6 0^{\circ}

to the right side

6 0^{\circ} - a = arcsin (0.598) + 36 0^{\circ} n

Subtract

6 0^{\circ}

from both sides

6 0^{\circ} - a - 6 0^{\circ} = arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

Simplify

- a = arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

- a = arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

Divide both sides by

- 1

- a = arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

Divide both sides by

- 1

\frac{- a}{- 1} = \frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Simplify

\frac{- a}{- 1} = \frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Simplify

\frac{- a}{- 1} : a

\frac{- a}{- 1}

Apply the fraction rule:

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

= \frac{a}{1}

Apply rule

\frac{a}{1} = a

= a

Simplify

\frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598)

\frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Group like terms

= \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1} + \frac{arcsin ( 0.598 )}{- 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{6 0 ^{\circ}}{- 1} + \frac{arcsin ( 0.598 )}{- 1}

\frac{6 0 ^{\circ}}{- 1} = - 6 0^{\circ}

\frac{6 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - \frac{6 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{6 0 ^{\circ}}{1} = 6 0^{\circ}

= - 6 0^{\circ}

\frac{arcsin ( 0.598 )}{- 1} = - arcsin (0.598)

\frac{arcsin ( 0.598 )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.598 )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.598)

= - 36 0^{\circ} n - (- 6 0^{\circ}) - arcsin (0.598)

Apply rule

- (- a) = a

= - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598)

a = - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598)

a = - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598)

a = - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598)

Solve

6 0^{\circ} - a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n : a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

6 0^{\circ} - a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n

Move

6 0^{\circ}

to the right side

6 0^{\circ} - a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n

Subtract

6 0^{\circ}

from both sides

6 0^{\circ} - a - 6 0^{\circ} = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

Simplify

- a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

- a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

Divide both sides by

- 1

- a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n - 6 0^{\circ}

Divide both sides by

- 1

\frac{- a}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Simplify

\frac{- a}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Simplify

\frac{- a}{- 1} : a

\frac{- a}{- 1}

Apply the fraction rule:

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

= \frac{a}{1}

Apply rule

\frac{a}{1} = a

= a

Simplify

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.598 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Group like terms

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.598 )}{- 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{6 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.598 )}{- 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{6 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.598 )}{- 1}

\frac{6 0 ^{\circ}}{- 1} = - 6 0^{\circ}

\frac{6 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - \frac{6 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{6 0 ^{\circ}}{1} = 6 0^{\circ}

= - 6 0^{\circ}

\frac{arcsin ( 0.598 )}{- 1} = - arcsin (0.598)

\frac{arcsin ( 0.598 )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.598 )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.598)

= - 18 0^{\circ} - 36 0^{\circ} n - (- 6 0^{\circ}) - (- arcsin (0.598))

Apply rule

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

a = - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598), a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

Show solutions in decimal form

a = - 36 0^{\circ} n + 6 0^{\circ} - 0.64100 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + 0.64100 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for sin(60-a)=0.598 ?
The general solution for sin(60-a)=0.598 is a=-360n+60-0.64100…,a=-180-360n+60+0.64100…