What is the general solution for 7/2 =3sin(b(pi/2))+2 ?

The general solution for 7/2 =3sin(b(pi/2))+2 is b= 1/3+4n,b= 5/3+4n

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7/2 =3sin(b(pi/2))+2

Solution

\frac{7}{2} = 3 sin (b (\frac{π}{2})) + 2

Solution

b = \frac{1}{3} + 4 n, b = \frac{5}{3} + 4 n

Degrees

b = 19.09859 \dots^{\circ} + 229.18311 \dots^{\circ} n, b = 95.49296 \dots^{\circ} + 229.18311 \dots^{\circ} n

Solution steps

\frac{7}{2} = 3 sin (b (\frac{π}{2})) + 2

Switch sides

3 sin (b \frac{π}{2}) + 2 = \frac{7}{2}

Move

2

to the right side

3 sin (b \frac{π}{2}) + 2 = \frac{7}{2}

Subtract

2

from both sides

3 sin (b \frac{π}{2}) + 2 - 2 = \frac{7}{2} - 2

Simplify

3 sin (b \frac{π}{2}) + 2 - 2 = \frac{7}{2} - 2

Simplify

3 sin (b \frac{π}{2}) + 2 - 2 : 3 sin (b \frac{π}{2})

3 sin (b \frac{π}{2}) + 2 - 2

Add similar elements:

2 - 2 = 0

= 3 sin (b \frac{π}{2})

Simplify

\frac{7}{2} - 2 : \frac{3}{2}

\frac{7}{2} - 2

Convert element to fraction:

2 = \frac{2 \cdot 2}{2}

= - \frac{2 \cdot 2}{2} + \frac{7}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 2 \cdot 2 + 7}{2}

- 2 \cdot 2 + 7 = 3

- 2 \cdot 2 + 7

Multiply the numbers:

2 \cdot 2 = 4

= - 4 + 7

Add/Subtract the numbers:

- 4 + 7 = 3

= 3

= \frac{3}{2}

3 sin (b \frac{π}{2}) = \frac{3}{2}

3 sin (b \frac{π}{2}) = \frac{3}{2}

3 sin (b \frac{π}{2}) = \frac{3}{2}

Divide both sides by

3

3 sin (b \frac{π}{2}) = \frac{3}{2}

Divide both sides by

3

\frac{3 sin ( b \frac{π}{2} )}{3} = \frac{\frac{3}{2}}{3}

Simplify

\frac{3 sin ( b \frac{π}{2} )}{3} = \frac{\frac{3}{2}}{3}

Simplify

\frac{3 sin ( b \frac{π}{2} )}{3} : sin (b \frac{π}{2})

\frac{3 sin ( b \frac{π}{2} )}{3}

Divide the numbers:

\frac{3}{3} = 1

= sin (b \frac{π}{2})

Simplify

\frac{\frac{3}{2}}{3} : \frac{1}{2}

\frac{\frac{3}{2}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{3}{6}

Cancel the common factor:

3

= \frac{1}{2}

sin (b \frac{π}{2}) = \frac{1}{2}

sin (b \frac{π}{2}) = \frac{1}{2}

sin (b \frac{π}{2}) = \frac{1}{2}

General solutions for

sin (b \frac{π}{2}) = \frac{1}{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{π}{2} = \frac{π}{6} + 2 πn, b \frac{π}{2} = \frac{5 π}{6} + 2 πn

b \frac{π}{2} = \frac{π}{6} + 2 πn, b \frac{π}{2} = \frac{5 π}{6} + 2 πn

Solve

b \frac{π}{2} = \frac{π}{6} + 2 πn : b = \frac{1}{3} + 4 n

b \frac{π}{2} = \frac{π}{6} + 2 πn

Multiply both sides by

2

b \frac{π}{2} = \frac{π}{6} + 2 πn

Multiply both sides by

2

2 b \frac{π}{2} = 2 \cdot \frac{π}{6} + 2 \cdot 2 πn

Simplify

2 b \frac{π}{2} = 2 \cdot \frac{π}{6} + 2 \cdot 2 πn

Simplify

2 b \frac{π}{2} : πb

2 b \frac{π}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 π}{2} b

Cancel the common factor:

2

= bπ

Simplify

2 \cdot \frac{π}{6} + 2 \cdot 2 πn : \frac{π}{3} + 4 πn

2 \cdot \frac{π}{6} + 2 \cdot 2 πn

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{6}

Cancel the common factor:

2

= \frac{π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= \frac{π}{3} + 4 πn

πb = \frac{π}{3} + 4 πn

πb = \frac{π}{3} + 4 πn

πb = \frac{π}{3} + 4 πn

Divide both sides by

π

πb = \frac{π}{3} + 4 πn

Divide both sides by

π

\frac{πb}{π} = \frac{\frac{π}{3}}{π} + \frac{4 πn}{π}

Simplify

\frac{πb}{π} = \frac{\frac{π}{3}}{π} + \frac{4 πn}{π}

Simplify

\frac{πb}{π} : b

\frac{πb}{π}

Cancel the common factor:

π

= b

Simplify

\frac{\frac{π}{3}}{π} + \frac{4 πn}{π} : \frac{1}{3} + 4 n

\frac{\frac{π}{3}}{π} + \frac{4 πn}{π}

\frac{\frac{π}{3}}{π} = \frac{1}{3}

\frac{\frac{π}{3}}{π}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 π}

Cancel the common factor:

π

= \frac{1}{3}

\frac{4 πn}{π} = 4 n

\frac{4 πn}{π}

Cancel the common factor:

π

= 4 n

= \frac{1}{3} + 4 n

b = \frac{1}{3} + 4 n

b = \frac{1}{3} + 4 n

b = \frac{1}{3} + 4 n

Solve

b \frac{π}{2} = \frac{5 π}{6} + 2 πn : b = \frac{5}{3} + 4 n

b \frac{π}{2} = \frac{5 π}{6} + 2 πn

Multiply both sides by

2

b \frac{π}{2} = \frac{5 π}{6} + 2 πn

Multiply both sides by

2

2 b \frac{π}{2} = 2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

Simplify

2 b \frac{π}{2} = 2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

Simplify

2 b \frac{π}{2} : πb

2 b \frac{π}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 π}{2} b

Cancel the common factor:

2

= bπ

Simplify

2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn : \frac{5 π}{3} + 4 πn

2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π 2}{6}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 π}{6}

Cancel the common factor:

2

= \frac{5 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= \frac{5 π}{3} + 4 πn

πb = \frac{5 π}{3} + 4 πn

πb = \frac{5 π}{3} + 4 πn

πb = \frac{5 π}{3} + 4 πn

Divide both sides by

π

πb = \frac{5 π}{3} + 4 πn

Divide both sides by

π

\frac{πb}{π} = \frac{\frac{5 π}{3}}{π} + \frac{4 πn}{π}

Simplify

\frac{πb}{π} = \frac{\frac{5 π}{3}}{π} + \frac{4 πn}{π}

Simplify

\frac{πb}{π} : b

\frac{πb}{π}

Cancel the common factor:

π

= b

Simplify

\frac{\frac{5 π}{3}}{π} + \frac{4 πn}{π} : \frac{5}{3} + 4 n

\frac{\frac{5 π}{3}}{π} + \frac{4 πn}{π}

\frac{\frac{5 π}{3}}{π} = \frac{5}{3}

\frac{\frac{5 π}{3}}{π}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{5 π}{3 π}

Cancel the common factor:

π

= \frac{5}{3}

\frac{4 πn}{π} = 4 n

\frac{4 πn}{π}

Cancel the common factor:

π

= 4 n

= \frac{5}{3} + 4 n

b = \frac{5}{3} + 4 n

b = \frac{5}{3} + 4 n

b = \frac{5}{3} + 4 n

b = \frac{1}{3} + 4 n, b = \frac{5}{3} + 4 n

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Frequently Asked Questions (FAQ)

What is the general solution for 7/2 =3sin(b(pi/2))+2 ?
The general solution for 7/2 =3sin(b(pi/2))+2 is b= 1/3+4n,b= 5/3+4n