What is the general solution for 4sin(B)+sqrt(8)=0 ?

The general solution for 4sin(B)+sqrt(8)=0 is B=(5pi)/4+2pin,B=(7pi)/4+2pin

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Popular >

4sin(B)+sqrt(8)=0

Solution

4 sin (B) + 8 = 0

Solution

B = \frac{5 π}{4} + 2 πn, B = \frac{7 π}{4} + 2 πn

Degrees

B = 22 5^{\circ} + 36 0^{\circ} n, B = 31 5^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (B) + 8 = 0

Simplify

4 sin (B) + 8 : 4 sin (B) + 22

4 sin (B) + 8

8 = 22

8

Prime factorization of

8 : 2^{3}

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

2

is a prime number, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2

= 2^{3}

= 2^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= 2^{2} \cdot 2

Apply radical rule:

= 2 2^{2}

Apply radical rule:

2^{2} = 2

= 22

= 4 sin (B) + 22

4 sin (B) + 22 = 0

Move

22

to the right side

4 sin (B) + 22 = 0

Subtract

22

from both sides

4 sin (B) + 22 - 22 = 0 - 22

Simplify

4 sin (B) = - 22

4 sin (B) = - 22

Divide both sides by

4

4 sin (B) = - 22

Divide both sides by

4

\frac{4 sin ( B )}{4} = \frac{- 2 2}{4}

Simplify

\frac{4 sin ( B )}{4} = \frac{- 2 2}{4}

Simplify

\frac{4 sin ( B )}{4} : sin (B)

\frac{4 sin ( B )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (B)

Simplify

\frac{- 2 2}{4} : - \frac{2}{2}

\frac{- 2 2}{4}

Apply the fraction rule:

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

= - \frac{2 2}{4}

Cancel the common factor:

2

= - \frac{2}{2}

sin (B) = - \frac{2}{2}

sin (B) = - \frac{2}{2}

sin (B) = - \frac{2}{2}

General solutions for

sin (B) = - \frac{2}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

B = \frac{5 π}{4} + 2 πn, B = \frac{7 π}{4} + 2 πn

B = \frac{5 π}{4} + 2 πn, B = \frac{7 π}{4} + 2 πn

Popular Examples

4cos(x)-5=-7

4 cos (x) - 5 = - 7

0=1+2sin((x^2)/2)

0 = 1 + 2 sin (\frac{x ^{2}}{2})

cos(2x)-5cos(x)+3=0

cos (2 x) - 5 cos (x) + 3 = 0

9sin^2(x)+18sin(x)+9=0

9 sin^{2} (x) + 18 sin (x) + 9 = 0

-12sin^2(θ)+7=4

- 12 sin^{2} (θ) + 7 = 4

Frequently Asked Questions (FAQ)

What is the general solution for 4sin(B)+sqrt(8)=0 ?
The general solution for 4sin(B)+sqrt(8)=0 is B=(5pi)/4+2pin,B=(7pi)/4+2pin