Trigonometri - Svendborg Erhvervsskole

Trigonometri – former for vilkårlige trekanter.
Sinusrelation:
a
sin (A)
a
sin (A)
b
sin (B)
a
sin (A)
b
c
= = = 2R
sin (B) sin (C)
=
=
=
Cosinusrelation:
b
sin (B)
c
sin (C)
c
sin (C)
*********************************
cos A = b 2 + c 2 - a 2 a 2 = b 2 + c 2 – 2 • b • c • cos A
2 • b • c
cos B = a 2 + c 2 - b 2 b 2 = a 2 + c 2 – 2 • a • c • cos B
2 • a • c
cos C = a 2 + b 2 - c 2 c 2 = a 2 + b 2 – 2 • a • b • cos C
2 • a • b
***********************************
Arealformler:
A = ½ • a • b • sin C Herons formel:
A = ½ • a • c • sin B A = s • (s – a) • (s – b) • (s – c)
A = ½ • b • c • sin A
s = a + b + c
2
Svendborg Erhvervsskole Tømrerafdelingen Matematik Niels Mark Aagaard Side 11 af 12
A
R
B
C