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Popular Trigonometry >

3sin^2(c)-7sin(x)+2=0

Solution

3 sin^{2} (c) - 7 sin (x) + 2 = 0

Solution

x = arcsin (- \frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn, x = π + arcsin (\frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn

Solution steps

3 sin^{2} (c) - 7 sin (x) + 2 = 0

Move

3 sin^{2} (c)

to the right side

3 sin^{2} (c) - 7 sin (x) + 2 = 0

Subtract

3 sin^{2} (c)

from both sides

3 sin^{2} (c) - 7 sin (x) + 2 - 3 sin^{2} (c) = 0 - 3 sin^{2} (c)

Simplify

- 7 sin (x) + 2 = - 3 sin^{2} (c)

- 7 sin (x) + 2 = - 3 sin^{2} (c)

Move

2

to the right side

- 7 sin (x) + 2 = - 3 sin^{2} (c)

Subtract

2

from both sides

- 7 sin (x) + 2 - 2 = - 3 sin^{2} (c) - 2

Simplify

- 7 sin (x) = - 3 sin^{2} (c) - 2

- 7 sin (x) = - 3 sin^{2} (c) - 2

Divide both sides by

- 7

- 7 sin (x) = - 3 sin^{2} (c) - 2

Divide both sides by

- 7

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

Simplify

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

Simplify

\frac{- 7 sin ( x )}{- 7} : sin (x)

\frac{- 7 sin ( x )}{- 7}

Apply the fraction rule:

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

= \frac{7 sin ( x )}{7}

Divide the numbers:

\frac{7}{7} = 1

= sin (x)

Simplify

- \frac{3 sin ^{2} ( c )}{- 7} - \frac{2}{- 7} : - \frac{- 3 sin ^{2} ( c ) - 2}{7}

- \frac{3 sin ^{2} ( c )}{- 7} - \frac{2}{- 7}

Apply rule

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

= \frac{- 3 sin ^{2} ( c ) - 2}{- 7}

Apply the fraction rule:

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

= - \frac{- 3 sin ^{2} ( c ) - 2}{7}

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arcsin (- \frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn, x = π + arcsin (\frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn

x = arcsin (- \frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn, x = π + arcsin (\frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn

Graph

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