What is the general solution for sin(90-a)= 1/(1.63) ?

The general solution for sin(90-a)= 1/(1.63) is a=-360n+90-0.66048…,a=-180-360n+90+0.66048…

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Popular >

sin(90-a)= 1/(1.63)

Solution

sin (9 0^{\circ} - a) = \frac{1}{1.63}

Solution

a = - 36 0^{\circ} n + 9 0^{\circ} - 0.66048 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.66048 \dots

Radians

a = \frac{π}{2} - 0.66048 \dots - 2 πn, a = - π + \frac{π}{2} + 0.66048 \dots - 2 πn

Solution steps

sin (9 0^{\circ} - a) = \frac{1}{1.63}

Apply trig inverse properties

sin (9 0^{\circ} - a) = \frac{1}{1.63}

General solutions for

sin (9 0^{\circ} - a) = \frac{1}{1.63}

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

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n, 9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n, 9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

Solve

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n : a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

Move

9 0^{\circ}

to the right side

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

Subtract

9 0^{\circ}

from both sides

9 0^{\circ} - a - 9 0^{\circ} = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

Simplify

- a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

- a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

- a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

\frac{- a}{- 1} = \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- a}{- 1} = \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 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 ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

\frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Group like terms

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} + \frac{arcsin ( \frac{1}{1.63} )}{- 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{9 0 ^{\circ}}{- 1} + \frac{arcsin ( \frac{1}{1.63} )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - \frac{9 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{arcsin ( \frac{1}{1.63} )}{- 1} = - arcsin (\frac{1}{1.63})

\frac{arcsin ( \frac{1}{1.63} )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( \frac{1}{1.63} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{arcsin ( \frac{1}{1.63} )}{1} = arcsin (\frac{1}{1.63})

= - arcsin (\frac{1}{1.63})

= - 36 0^{\circ} n - (- 9 0^{\circ}) - arcsin (\frac{1}{1.63})

Apply rule

- (- a) = a

= - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

Solve

9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n : a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

Move

9 0^{\circ}

to the right side

9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

Subtract

9 0^{\circ}

from both sides

9 0^{\circ} - a - 9 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

Simplify

- a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

- a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

- a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

\frac{- a}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- a}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 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 ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Group like terms

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 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{9 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 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{9 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - \frac{9 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{arcsin ( \frac{1}{1.63} )}{- 1} = - arcsin (\frac{1}{1.63})

\frac{arcsin ( \frac{1}{1.63} )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( \frac{1}{1.63} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{arcsin ( \frac{1}{1.63} )}{1} = arcsin (\frac{1}{1.63})

= - arcsin (\frac{1}{1.63})

= - 18 0^{\circ} - 36 0^{\circ} n - (- 9 0^{\circ}) - (- arcsin (\frac{1}{1.63}))

Apply rule

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63}), a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

Show solutions in decimal form

a = - 36 0^{\circ} n + 9 0^{\circ} - 0.66048 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.66048 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for sin(90-a)= 1/(1.63) ?
The general solution for sin(90-a)= 1/(1.63) is a=-360n+90-0.66048…,a=-180-360n+90+0.66048…