Question

Oblicz pozostałe wartości funkcji trygonometrycznych kąta ostrego alfa jeśli
a)tg alfa=3/4
b)sin alfa=5/13
c)cos alfa=1/4
d)tg alfa=11/60

Answer 1

A)tgα=3/4
ctgα=4/3

1+tg²α=1/cos²α
1+(3/4)²=1/cos²α
25/16=1/cos²α
cos²α=16/25
cosα=4/5
sin²α+cos²α=1
sin²α=1-cos²α
sin²α=1-16/25
sin²α=9/25
sinα=3/5

b) sinα=5/13
sin²α+cos²α=1
cos²α=1-25/169
cosα=12/13
tgα=cosα/sinα
tgα=12/13 : 5/13
tgα=12/5
ctgα=5/12
c)cosα=1/4
sin²α+cos²α=1
sin²α=1-1/16
sinα=√15/4
tgα=cosα/sinα
tgα= 1/4 : √15/4
tgα=√15/15
ctgα=√15

d) tgα=11/60
ctgα=60/11
1+tg²α=1/cos²α
3721/3600=1/cos²α
cos²α=3600/3721
cosα=60/61
sin²α=1-cos²α
sin²α=1-3600/3721
sin²α=121/3721
sinα=11/61