Question

Calcular aproximadamente tangente de 42

Answer 1

Respuesta:

$tg42=\dfrac{10296}{11753}$

tg 42° ≈ 0,876

Explicación paso a paso:

tg 42° = tg 2(21°)

Calculamos primero tg 21° aplicando tangente de la diferencia de ángulos ::

tg 21° = tg(37° - 16°)

$tg21=\dfrac{tg37-tg16}{1+tg37.tg16}=\dfrac{\dfrac{3}{4} -\dfrac{7}{24} }{1+(\dfrac{3}{4} )(\dfrac{7}{24} )}=\dfrac{\dfrac{11}{24} }{1+\dfrac{7}{32} }=\dfrac{\dfrac{11}{24}}{\dfrac{39}{32}} =\dfrac{44}{117}$

Calculamos tg 42° utilizando tangente del doble de un ángulo :

tg 42° = tg 2(21°)

$tg42=\dfrac{2tg21}{1-tg^{2} 21} =\dfrac{2(\dfrac{44}{117} )}{1-(\dfrac{44}{117})^{2} }=\dfrac{\dfrac{88}{117} }{\dfrac{117^{2}-44^{2}}{117^{2}} }=\dfrac{\dfrac{88}{117} }{\dfrac{11753}{117^{2}} }=\dfrac{10296}{11753}$