Odpowiedź:
Niech a = alfa
1.
a)tg a = sin a/cos a = 3/5 : 4/5 = 3/4
b)tg a = sin a/cos a = [tex]\sqrt{5}[/tex]/5 : 2
2.
a)tg a = sin a/cos a
[tex]\frac{3}{4}[/tex] = [tex]\frac{3}{5}[/tex] / x /*x
[tex]\frac{3}{4}[/tex] x = [tex]\frac{3}{5}[/tex] /:
x = [tex]\frac{3}{5}[/tex] / [tex]\frac{3}{4}[/tex]
x = [tex]\frac{4}{5}[/tex]
b)tg a = sin a/cos a
[tex]\frac{12}{5}[/tex] = x / [tex]\frac{5}{13}[/tex] /*
x = [tex]\frac{12}{5}[/tex] * [tex]\frac{5}{13}[/tex]
x = [tex]\frac{12}{13}[/tex]
3.
[tex]sin^{2}[/tex] a + [tex]cos^{2}[/tex] a = 1 Korzystam z tożsamości - jednyki trygonometrycznej
a)
[tex]1/3^{2}[/tex] + [tex]cos^{2}[/tex] a = 1
1/9 + [tex]cos^{2}[/tex] a = 1 /- 1/9
[tex]cos^{2}[/tex] a = 8/9 /[tex]\sqrt{}[/tex]
cos a = [tex]\sqrt{8}[/tex] / 3
tg a = [tex]\frac{sin a}{cos a}[/tex]
tg a = 1/3 : [tex]\sqrt{8}[/tex] / 3
tg a = 1 / [tex]\sqrt{8}[/tex] = [tex]\sqrt{8}[/tex] / 8
ctg a = [tex]\sqrt{8}[/tex] ponieważ jest to odwrotność tangensa
b)
[tex]3/5^{2}[/tex] + [tex]cos^{2}[/tex] a = 1
[tex]\frac{9}{25}[/tex] + [tex]cos^{2}[/tex] a = 1 /-
[tex]cos^{2}[/tex] a = [tex]\frac{16}{25}[/tex] /[tex]\sqrt{}[/tex]
cos a = [tex]\frac{4}{5}[/tex]
tg a = [tex]\frac{3/5}{4/5}[/tex] = [tex]\frac{3}{4}[/tex]
ctg a = [tex]\frac{4}{3}[/tex]
c)
[tex]sin^{2}[/tex] a + ( [tex]\frac{4}{5}[/tex] ) [tex]^{2}[/tex] = 1
[tex]sin^{2}[/tex] a + [tex]\frac{16}{25}[/tex] = 1 /-
[tex]sin^{2}[/tex] a = [tex]\frac{9}{25}[/tex] /[tex]\sqrt{}[/tex]
sin a = [tex]\frac{3}{5}[/tex]
tg a = [tex]\frac{3/5}{4/5}[/tex] = [tex]\frac{3}{4}[/tex]
ctg a = [tex]\frac{4}{3}[/tex]
d)
[tex]sin^{2}[/tex] a + ( [tex]\frac{3}{5}[/tex] ) [tex]^{2}[/tex] = 1
[tex]sin^{2}[/tex] a + [tex]\frac{9}{25}[/tex] = 1 /-
[tex]sin^{2}[/tex] a = [tex]\frac{16}{25}[/tex] /[tex]\sqrt{}[/tex]
sin a = [tex]\frac{4}{5}[/tex]
tg a = [tex]\frac{3/5}{4/5}[/tex] = [tex]\frac{3}{4}[/tex]
ctg a = [tex]\frac{4}{3}[/tex]
Szczegółowe wyjaśnienie:
