What is the general solution for sin(a)=(((8))/((sqrt(153)))) ?

The general solution for sin(a)=(((8))/((sqrt(153)))) is a=0.70333…+2pin,a=pi-0.70333…+2pin

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sin(a)=(((8))/((sqrt(153))))

sin (a) = (\frac{( 8 )}{( 153 )})

a = 0.70333 \dots + 2 πn, a = π - 0.70333 \dots + 2 πn

Radians

a = 0.70333 \dots + 6.28318 \dots n, a = π - 0.70333 \dots + 6.28318 \dots n

Solution steps

sin (a) = (\frac{( 8 )}{( 153 )})

Simplify

\frac{8}{153} : \frac{8 17}{51}

\frac{8}{153}

153 = 317

153

Prime factorization of

153 : 3^{2} \cdot 17

153

153

divides by

3153 = 51 \cdot 3

= 3 \cdot 51

51

divides by

351 = 17 \cdot 3

= 3 \cdot 3 \cdot 17

3, 17

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 17

= 3^{2} \cdot 17

= 3^{2} \cdot 17

Apply radical rule:

= 17 3^{2}

Apply radical rule:

3^{2} = 3

= 317

= \frac{8}{3 17}

Rationalize

\frac{8}{3 17} : \frac{8 17}{51}

\frac{8}{3 17}

Multiply by the conjugate

\frac{17}{17}

= \frac{8 17}{3 17 17}

31717 = 51

31717

Apply radical rule:

a a = a

1717 = 17

= 3 \cdot 17

Multiply the numbers:

3 \cdot 17 = 51

= 51

= \frac{8 17}{51}

= \frac{8 17}{51}

sin (a) = \frac{8 17}{51}

Apply trig inverse properties

sin (a) = \frac{8 17}{51}

General solutions for

sin (a) = \frac{8 17}{51}

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

a = arcsin (\frac{8 17}{51}) + 2 πn, a = π - arcsin (\frac{8 17}{51}) + 2 πn

a = arcsin (\frac{8 17}{51}) + 2 πn, a = π - arcsin (\frac{8 17}{51}) + 2 πn

Show solutions in decimal form

a = 0.70333 \dots + 2 πn, a = π - 0.70333 \dots + 2 πn

2 csc^{2} (x) - 1 = 0

- sec (θ) cot (θ) - sec (θ) = - 2 sec (θ)

sec^{2} (a) = \frac{4}{3}

sin (5 x - 27) = cos (6 x + 13.6)

sin (x) = \frac{1}{cos ( - 10 0 ^{\circ} )}

What is the general solution for sin(a)=(((8))/((sqrt(153)))) ?
The general solution for sin(a)=(((8))/((sqrt(153)))) is a=0.70333…+2pin,a=pi-0.70333…+2pin