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sin(θ)=(0.000069)2(500*10^{-9})

Solution

sin (θ) = (0.000069) 2 (500 \cdot 1 0^{- 9})

θ = 0 + 2 πn, θ = π - 0 + 2 πn

Radians

θ = 0 + 2 πn, θ = π + 2 πn

étapes des solutions

sin (θ) = (0.000069) \cdot 2 (500 \cdot 1 0^{- 9})

Simplifier

0.000069 \cdot 2 \cdot 500 \cdot 1 0^{- 9} : \frac{0.000069}{1000000}

0.000069 \cdot 2 \cdot 500 \cdot 1 0^{- 9}

Appliquer la règle de l'exposant:

a^{- b} = \frac{1}{a ^{b}}

1 0^{- 9} = \frac{1}{1 0 ^{9}}

= 2 \cdot 500 \cdot 0.000069 \cdot \frac{1}{1 0 ^{9}}

Multiplier des fractions:

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

= 0.000069 \cdot \frac{1 \cdot 2 \cdot 500}{1 0 ^{9}}

\frac{1 \cdot 2 \cdot 500}{1 0 ^{9}} = \frac{1}{1000000}

\frac{1 \cdot 2 \cdot 500}{1 0 ^{9}}

Multiplier les nombres :

1 \cdot 2 \cdot 500 = 1000

= \frac{1000}{1 0 ^{9}}

Factoriser

1000 : 2^{3} \cdot 5^{3}

Factoriser

1000 = 2^{3} \cdot 5^{3}

Factoriser

1 0^{9} : 2^{9} \cdot 5^{9}

Factoriser

10 = 2 \cdot 5

= (2 \cdot 5)^{9}

Appliquer la règle de l'exposant:

(ab)^{c} = a^{c} b^{c}

= 2^{9} \cdot 5^{9}

= \frac{2 ^{3} \cdot 5 ^{3}}{2 ^{9} \cdot 5 ^{9}}

Annuler

\frac{2 ^{3} \cdot 5 ^{3}}{2 ^{9} \cdot 5 ^{9}} : \frac{1}{2 ^{6} \cdot 5 ^{6}}

\frac{2 ^{3} \cdot 5 ^{3}}{2 ^{9} \cdot 5 ^{9}}

Appliquer la règle de l'exposant:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{3}}{2 ^{9}} = \frac{1}{2 ^{9 - 3}}

= \frac{5 ^{3}}{5 ^{9} \cdot 2 ^{9 - 3}}

Soustraire les nombres :

9 - 3 = 6

= \frac{5 ^{3}}{5 ^{9} \cdot 2 ^{6}}

Appliquer la règle de l'exposant:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{5 ^{3}}{5 ^{9}} = \frac{1}{5 ^{9 - 3}}

= \frac{1}{2 ^{6} \cdot 5 ^{9 - 3}}

Soustraire les nombres :

9 - 3 = 6

= \frac{1}{2 ^{6} \cdot 5 ^{6}}

= \frac{1}{2 ^{6} \cdot 5 ^{6}}

2^{6} \cdot 5^{6} = 1000000

2^{6} \cdot 5^{6}

2^{6} = 64

= 5^{6} \cdot 64

5^{6} = 15625

= 64 \cdot 15625

Multiplier les nombres :

64 \cdot 15625 = 1000000

= 1000000

= \frac{1}{1000000}

= 0.000069 \cdot \frac{1}{1000000}

Multiplier des fractions:

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

= \frac{1 \cdot 0.000069}{1000000}

Multiplier les nombres :

1 \cdot 0.000069 = 0.000069

= \frac{0.000069}{1000000}

Appliquer les propriétés trigonométriques inverses

sin (θ) = \frac{0.000069}{1000000}

Solutions générales pour

sin (θ) = \frac{0.000069}{1000000}

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

θ = arcsin (\frac{0.000069}{1000000}) + 2 πn, θ = π - arcsin (\frac{0.000069}{1000000}) + 2 πn

θ = arcsin (\frac{0.000069}{1000000}) + 2 πn, θ = π - arcsin (\frac{0.000069}{1000000}) + 2 πn

Montrer les solutions sous la forme décimale

θ = 0 + 2 πn, θ = π - 0 + 2 πn

(2 sin^{2} (x) - 1) (tan (x) - 1) = 0

(csc (x) + 2) (csc (x) - 2) = 0, 0 \leq x \leq 2 π

cos (x) = 55

cos (x) = 35

sin (x) = \frac{12}{10}