Question

Halla el valor numérico de:
csc 30° + sec 30° + tan 45°

Answer 1

Recordemos

Cosecante (Csc) es el inverso del seno es decir:

Csc 30° = 1/(Sen 30°)

sen 30° = 1/2

Csc 30° = 1/(1/2) = 2

Secante (sec) es el inverso del coseno

Sec 30° = 1/Cos 30°

Cos 30° = (√3)/2

Sec 30° = 1/[(√3)/2]

Sec 30° = 2/(√3) => Racionalizamos

$\frac{2}{ \sqrt{3}}* \frac{ \sqrt{3} }{ \sqrt{3} }$

$\frac{2 \sqrt{3} }{( \sqrt{3})( \sqrt{3})} = \frac{2 \sqrt{3}}{3}$

Sec 30° = [2√3]/3

Tan 45° = 1

csc 30° + sec 30° + tan 45°  = 2 + [2√3]/3 + 1


2 + [2√3]/3 + 1 = [2(3) + (2√3) + 1(3)]/3

= [6 + (2√3) + 3]/3

= [9 + (2√3)]/3

= 3 + (2√3)/3

3 + (2√3)/3 ≈ 4.1547005