Bedste svar
sin (theta) = a / c
csc (theta) = 1 / sin (theta) = c / a
cos (theta) = b / c
sek ( theta) = 1 / cos (theta) = c / b
tan (theta) = sin (theta) / cos (theta) = a / b
barneseng (theta) = 1 / tan (theta) = b / a
sin (-x) = -sin (x) csc (-x) = -csc (x) cos (-x) = cos (x) sek (-x) = sec (x) tan (-x) = -tan (x) barneseng (-x) = -cot (x)
sin ^ 2 (x) + cos ^ 2 (x ) = 1
tan ^ 2 (x) + 1 = sec ^ 2 (x)
barneseng ^ 2 (x) + 1 = csc ^ 2 (x)
sin (xy) = sin x cos y cos x sin y
cos (xy) = cos x hyggelig sin x sin y
Trigonometriske identiteter
( Matematik | Trig | Identiteter)
sin (theta) = a / c
csc (theta) = 1 / sin (theta) = c / a
cos (theta) = b / c
sec (theta) = 1 / cos (theta) = c / b
tan (theta) = sin (theta) / cos (theta) = a / b
barneseng (theta) = 1 / tan (theta) = b / a
sin (-x) = -sin (x) csc (-x) = -csc (x) cos (-x) = cos (x) sek (- x) = sec (x) tan (-x) = -tan (x) barneseng (-x) = -cot (x)
sin
^ 2
(x) + cos
^ 2
(x) = 1
tan
^ 2
(x) + 1 = sek
^ 2
(x)
barneseng
^ 2
(x) + 1 = csc
^ 2
(x)
sin (x
y) = sin x cos y
cos x sin y
cos (x
y) = cos x hyggelig
sin x sin y
tan (x
y) = (tan x
tan y) / (1
tan x tan y)
sin (2x) = 2 sin x cos x
cos (2x) = cos
^ 2
(x) – sin
^ 2
(x) = 2 cos
^ 2
(x) – 1 = 1-2 sin
^ 2
(x)
tan (2x) = 2 tan (x) / (1 – tan
^ 2
(x))
sin
^ 2
(x) = 1 / 2 – 1/2 cos (2x)
cos
^ 2
(x) = 1/2 + 1/2 cos (2x)
sin x – sin y = 2 sin ((x – y) / 2) cos ((x + y) / 2)
cos x – cos y = -2 sin ( (x – y) / 2) sin ((x + y) / 2)
Trig-tabel med fælles vinkler
vinkel
0
30
45
60
90
sin
^ 2
(a)
0/4
1/4
2/4
3/4
4/4
cos
^ 2
(a)
4/4
3 / 4
2/4
1/4
0/4
tan
^ 2
(a)
0/4
1/3
2/2
3/1
4/0
Svar
-seng (x)
Barneseng x er en ulige funktion, så udskiftning af x med -x ændrer funktionstegn