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Popular Trigonometría >

verificar sin^2(θ)+(1/2)^2=1

Solución

verificar

sin^{2} (θ) + (\frac{1}{2})^{2} = 1

Solución

Falso

Pasos de solución

sin^{2} (θ) + (\frac{1}{2})^{2} = 1

Demuestra que los dos lados no son iguales

Multiplicar

sin^{2} (θ) + (\frac{1}{2})^{2} = 1

por

θ = 0

sin^{2} (0) + (\frac{1}{2})^{2} = \frac{1}{4} (Decimal : 0.25)

sin^{2} (0) + (\frac{1}{2})^{2}

Utilizar la siguiente identidad trivial:

sin (0) = 0

sin (0)

tabla de valores periódicos con

2 πn

intervalos:

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}

= 0

= 0^{2} + (\frac{1}{2})^{2}

Simplificar

0^{2} + (\frac{1}{2})^{2} : \frac{1}{4}

0^{2} + (\frac{1}{2})^{2}

Aplicar la regla

0^{a} = 0

0^{2} = 0

= 0 + (\frac{1}{2})^{2}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Aplicar la regla

1^{a} = 1

1^{2} = 1

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

= 0 + \frac{1}{2 ^{2}}

0 + \frac{1}{2 ^{2}} = \frac{1}{2 ^{2}}

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

2^{2} = 4

= \frac{1}{4}

= \frac{1}{4}

Ambos lados no son iguales

\Rightarrow Falso

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