What is the general solution for sin(90-θ)=0.5745 ?

The general solution for sin(90-θ)=0.5745 is θ=-360n+90-0.61199…,θ=-180-360n+90+0.61199…

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Popular >

sin(90-θ)=0.5745

Solution

sin (9 0^{\circ} - θ) = 0.5745

Solution

θ = - 36 0^{\circ} n + 9 0^{\circ} - 0.61199 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.61199 \dots

Radians

θ = \frac{π}{2} - 0.61199 \dots - 2 πn, θ = - π + \frac{π}{2} + 0.61199 \dots - 2 πn

Solution steps

sin (9 0^{\circ} - θ) = 0.5745

Apply trig inverse properties

sin (9 0^{\circ} - θ) = 0.5745

General solutions for

sin (9 0^{\circ} - θ) = 0.5745

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

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n, 9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n, 9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

Solve

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n : θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n

Move

9 0^{\circ}

to the right side

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n

Subtract

9 0^{\circ}

from both sides

9 0^{\circ} - θ - 9 0^{\circ} = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Simplify

- θ = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

- θ = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

- θ = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

\frac{- θ}{- 1} = \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- θ}{- 1} = \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- θ}{- 1} : θ

\frac{- θ}{- 1}

Apply the fraction rule:

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

= \frac{θ}{1}

Apply rule

\frac{a}{1} = a

= θ

Simplify

\frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

\frac{arcsin ( 0.5745 )}{- 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 ( 0.5745 )}{- 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 ( 0.5745 )}{- 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 ( 0.5745 )}{- 1} = - arcsin (0.5745)

\frac{arcsin ( 0.5745 )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.5745 )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.5745)

= - 36 0^{\circ} n - (- 9 0^{\circ}) - arcsin (0.5745)

Apply rule

- (- a) = a

= - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

Solve

9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n : θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

Move

9 0^{\circ}

to the right side

9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

Subtract

9 0^{\circ}

from both sides

9 0^{\circ} - θ - 9 0^{\circ} = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Simplify

- θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

- θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

- θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- θ}{- 1} : θ

\frac{- θ}{- 1}

Apply the fraction rule:

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

= \frac{θ}{1}

Apply rule

\frac{a}{1} = a

= θ

Simplify

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 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 ( 0.5745 )}{- 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 ( 0.5745 )}{- 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 ( 0.5745 )}{- 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 ( 0.5745 )}{- 1} = - arcsin (0.5745)

\frac{arcsin ( 0.5745 )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.5745 )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.5745)

= - 18 0^{\circ} - 36 0^{\circ} n - (- 9 0^{\circ}) - (- arcsin (0.5745))

Apply rule

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745), θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

Show solutions in decimal form

θ = - 36 0^{\circ} n + 9 0^{\circ} - 0.61199 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.61199 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for sin(90-θ)=0.5745 ?
The general solution for sin(90-θ)=0.5745 is θ=-360n+90-0.61199…,θ=-180-360n+90+0.61199…