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sin^2(x)= 1/36

Solution

sin^{2} (x) = \frac{1}{36}

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn, x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

Degrés

x = 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 170.40593 \dots^{\circ} + 36 0^{\circ} n, x = - 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 189.59406 \dots^{\circ} + 36 0^{\circ} n

étapes des solutions

sin^{2} (x) = \frac{1}{36}

Résoudre par substitution

sin^{2} (x) = \frac{1}{36}

Soit :

sin (x) = u

u^{2} = \frac{1}{36}

u^{2} = \frac{1}{36} : u = \frac{1}{6}, u = - \frac{1}{6}

u^{2} = \frac{1}{36}

Pour

x^{2} = f (a)

les solutions sont

x = f (a), - f (a)

u = \frac{1}{36}, u = - \frac{1}{36}

\frac{1}{36} = \frac{1}{6}

\frac{1}{36}

Appliquer la règle des radicaux :

n \frac{a}{b} = \frac{n a}{n b},

en supposant

a \geq 0, b \geq 0

= \frac{1}{36}

36 = 6

36

Factoriser le nombre :

36 = 6^{2}

= 6^{2}

Appliquer la règle des radicaux:

n a^{n} = a

6^{2} = 6

= 6

= \frac{1}{6}

Appliquer la règle

1 = 1

= \frac{1}{6}

- \frac{1}{36} = - \frac{1}{6}

- \frac{1}{36}

Simplifier

\frac{1}{36} : \frac{1}{6}

\frac{1}{36}

Appliquer la règle des radicaux :

n \frac{a}{b} = \frac{n a}{n b},

en supposant

a \geq 0, b \geq 0

= \frac{1}{36}

36 = 6

36

Factoriser le nombre :

36 = 6^{2}

= 6^{2}

Appliquer la règle des radicaux:

n a^{n} = a

6^{2} = 6

= 6

= \frac{1}{6}

= - \frac{1}{6}

Appliquer la règle

1 = 1

= - \frac{1}{6}

u = \frac{1}{6}, u = - \frac{1}{6}

Remplacer

u = sin (x)

sin (x) = \frac{1}{6}, sin (x) = - \frac{1}{6}

sin (x) = \frac{1}{6}, sin (x) = - \frac{1}{6}

sin (x) = \frac{1}{6} : x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

sin (x) = \frac{1}{6}

Appliquer les propriétés trigonométriques inverses

sin (x) = \frac{1}{6}

Solutions générales pour

sin (x) = \frac{1}{6}

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

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

sin (x) = - \frac{1}{6} : x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

sin (x) = - \frac{1}{6}

Appliquer les propriétés trigonométriques inverses

sin (x) = - \frac{1}{6}

Solutions générales pour

sin (x) = - \frac{1}{6}

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

x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

Combiner toutes les solutions

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn, x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

Montrer les solutions sous la forme décimale

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn, x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

tan (x) = 31

sin^{4} (x) + cos^{2} (x) = 2

5 tan (x) = 15 cot (x)

x, arctan (x) = arctan (y)

cos (x + 1 0^{\circ}) - cos (x + 9 0^{\circ}) = 1