What is the general solution for 6sin(b)+sqrt(12)=0 ?

The general solution for 6sin(b)+sqrt(12)=0 is b=-0.61547…+2pin,b=pi+0.61547…+2pin

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Popular Trigonometry >

6sin(b)+sqrt(12)=0

Solution

6 sin (b) + 12 = 0

Solution

b = - 0.61547 \dots + 2 πn, b = π + 0.61547 \dots + 2 πn

Degrees

b = - 35.26438 \dots^{\circ} + 36 0^{\circ} n, b = 215.26438 \dots^{\circ} + 36 0^{\circ} n

Solution steps

6 sin (b) + 12 = 0

12 = 23

12

Prime factorization of

12 : 2^{2} \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

= 2^{2} \cdot 3

= 2^{2} \cdot 3

Apply radical rule:

n ab = n a n b

= 3 2^{2}

Apply radical rule:

n a^{n} = a

2^{2} = 2

= 23

6 sin (b) + 23 = 0

Move

23

to the right side

6 sin (b) + 23 = 0

Subtract

23

from both sides

6 sin (b) + 23 - 23 = 0 - 23

Simplify

6 sin (b) = - 23

6 sin (b) = - 23

Divide both sides by

6

6 sin (b) = - 23

Divide both sides by

6

\frac{6 sin ( b )}{6} = \frac{- 2 3}{6}

Simplify

\frac{6 sin ( b )}{6} = \frac{- 2 3}{6}

Simplify

\frac{6 sin ( b )}{6} : sin (b)

\frac{6 sin ( b )}{6}

Divide the numbers:

\frac{6}{6} = 1

= sin (b)

Simplify

\frac{- 2 3}{6} : - \frac{3}{3}

\frac{- 2 3}{6}

Apply the fraction rule:

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

= - \frac{2 3}{6}

Cancel the common factor:

2

= - \frac{3}{3}

sin (b) = - \frac{3}{3}

sin (b) = - \frac{3}{3}

sin (b) = - \frac{3}{3}

Apply trig inverse properties

sin (b) = - \frac{3}{3}

General solutions for

sin (b) = - \frac{3}{3}

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

b = arcsin (- \frac{3}{3}) + 2 πn, b = π + arcsin (\frac{3}{3}) + 2 πn

b = arcsin (- \frac{3}{3}) + 2 πn, b = π + arcsin (\frac{3}{3}) + 2 πn

Show solutions in decimal form

b = - 0.61547 \dots + 2 πn, b = π + 0.61547 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 6sin(b)+sqrt(12)=0 ?
The general solution for 6sin(b)+sqrt(12)=0 is b=-0.61547…+2pin,b=pi+0.61547…+2pin