es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

arcsin(3/5)+arccos(x)=pi

Solución

arcsin (\frac{3}{5}) + arccos (x) = π

Solución

x = - \frac{4}{5}

Pasos de solución

arcsin (\frac{3}{5}) + arccos (x) = π

Mover

arcsin (\frac{3}{5})

al lado derecho

arcsin (\frac{3}{5}) + arccos (x) = π

Restar

arcsin (\frac{3}{5})

de ambos lados

arcsin (\frac{3}{5}) + arccos (x) - arcsin (\frac{3}{5}) = π - arcsin (\frac{3}{5})

Simplificar

arccos (x) = π - arcsin (\frac{3}{5})

arccos (x) = π - arcsin (\frac{3}{5})

Aplicar propiedades trigonométricas inversas

arccos (x) = π - arcsin (\frac{3}{5})

arccos (x) = a \Rightarrow x = cos (a)

x = cos (π - arcsin (\frac{3}{5}))

cos (π - arcsin (\frac{3}{5})) = - \frac{4}{5}

cos (π - arcsin (\frac{3}{5}))

Re-escribir usando identidades trigonométricas:

cos (π) cos (arcsin (\frac{3}{5})) + sin (π) sin (arcsin (\frac{3}{5}))

cos (π - arcsin (\frac{3}{5}))

Utilizar la identidad de diferencia de ángulos:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (π) cos (arcsin (\frac{3}{5})) + sin (π) sin (arcsin (\frac{3}{5}))

= cos (π) cos (arcsin (\frac{3}{5})) + sin (π) sin (arcsin (\frac{3}{5}))

Utilizar la siguiente identidad trivial:

cos (π) = (- 1)

cos (π)

cos (x)

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

Re-escribir usando identidades trigonométricas:

cos (arcsin (\frac{3}{5})) = \frac{4}{5}

cos (arcsin (\frac{3}{5}))

Re-escribir usando identidades trigonométricas:

cos (arcsin (\frac{3}{5})) = 1 - (\frac{3}{5})^{2}

Usar la siguiente identidad:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{3}{5})^{2}

= 1 - (\frac{3}{5})^{2}

Simplificar

= \frac{4}{5}

Utilizar la siguiente identidad trivial:

sin (π) = 0

sin (π)

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

Re-escribir usando identidades trigonométricas:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

Usar la siguiente identidad:

sin (arcsin (x)) = x

= \frac{3}{5}

= (- 1) \frac{4}{5} + 0 \cdot \frac{3}{5}

Simplificar

= - \frac{4}{5}

x = - \frac{4}{5}

x = - \frac{4}{5}

Ejemplos populares

cos (θ) = \frac{6}{7}

2cos(2θ)+7sin(θ)=5

2 cos (2 θ) + 7 sin (θ) = 5

tan (x^{2}) = 1

cos (x) = \frac{5}{10}

cos^2(x)+9cos(x)+18=0

cos^{2} (x) + 9 cos (x) + 18 = 0