Question

Se cos(x)=2/5, calcule sen(x), tg(x), sec(x), cossec(x) e cotg(x).

Answer 1

sen²x + cos²x = 1
sen²x + (2/5)² = 1
sen²x = 1 - 4/25
sen²x = (25 - 4)/25
sen²x = 21/25
sen x = √21/25
sen x = √21 /5
tg x = sen x/cos x
tg x = (√21 /5) / (2/5)
tg x = (√21) / 2

sec x = 1 / cos x
sec x = 1 / (2/5)
sec x = 5/2

cossec x = 1 / sen x
cossec x = 1 / (√21 / 5)
cossec x = 5√21)( /21

cotag x = cos x / sen x
cotag x = (2/5) / (√21/5)
cotag x = (2√21) / 21