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

The general solution for (7pi)/2 =7-3sin(x) is No Solution for x\in\mathbb{R}

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Popular Trigonometry >

(7pi)/2 =7-3sin(x)

Solution

\frac{7 π}{2} = 7 - 3 sin (x)

Solution

No Solution for x \in R

Solution steps

\frac{7 π}{2} = 7 - 3 sin (x)

Switch sides

7 - 3 sin (x) = \frac{7 π}{2}

Move

7

to the right side

7 - 3 sin (x) = \frac{7 π}{2}

Subtract

7

from both sides

7 - 3 sin (x) - 7 = \frac{7 π}{2} - 7

Simplify

- 3 sin (x) = \frac{7 π}{2} - 7

- 3 sin (x) = \frac{7 π}{2} - 7

Divide both sides by

- 3

- 3 sin (x) = \frac{7 π}{2} - 7

Divide both sides by

- 3

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

Simplify

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

Simplify

\frac{- 3 sin ( x )}{- 3} : sin (x)

\frac{- 3 sin ( x )}{- 3}

Apply the fraction rule:

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

= \frac{3 sin ( x )}{3}

Divide the numbers:

\frac{3}{3} = 1

= sin (x)

Simplify

\frac{\frac{7 π}{2}}{- 3} - \frac{7}{- 3} : - \frac{7 π - 14}{6}

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

Apply rule

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

= \frac{\frac{7 π}{2} - 7}{- 3}

Apply the fraction rule:

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

= - \frac{\frac{7 π}{2} - 7}{3}

Join

\frac{7 π}{2} - 7 : \frac{7 π - 14}{2}

\frac{7 π}{2} - 7

Convert element to fraction:

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

= \frac{7 π}{2} - \frac{7 \cdot 2}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{7 π - 7 \cdot 2}{2}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{7 π - 14}{2}

= - \frac{\frac{7 π - 14}{2}}{3}

Simplify

\frac{\frac{7 π - 14}{2}}{3} : \frac{7 π - 14}{6}

\frac{\frac{7 π - 14}{2}}{3}

Apply the fraction rule:

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

= \frac{7 π - 14}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{7 π - 14}{6}

= - \frac{7 π - 14}{6}

sin (x) = - \frac{7 π - 14}{6}

sin (x) = - \frac{7 π - 14}{6}

sin (x) = - \frac{7 π - 14}{6}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for (7pi)/2 =7-3sin(x) ?
The general solution for (7pi)/2 =7-3sin(x) is No Solution for x\in\mathbb{R}