Trigonometric Identities
Trigonometric Identities
Pythagoras's theorem
sin2 + cos2 = 1
(1)
1 + cot2 = cosec2
(2)
tan2 + 1 = sec2
(3)
Note that (2) = (1)/ sin2 and (3) = (1)/ cos2 .
Compound-angle formulae
cos(A + B) = cos A cos B - sin A sin B
(4)
cos(A - B) = cos A cos B + sin A sin B
(5)
sin(A + B) = sin A cos B + cos A sin B
(6)
sin(A - B) = sin A cos B - cos A sin B
(7)
tan A + tan B
tan(A + B) =
(8)
1 - tan A tan B
tan(A - B) = tan A - tan B
(9)
1 + tan A tan B
cos 2 = cos2 - sin2 = 2 cos2 - 1 = 1 - 2 sin2
(10)
sin 2 = 2 sin cos
(11)
2 tan
tan 2 = 1 - tan2
(12)
Note that you can get (5) from (4) by replacing B with -B, and using the fact that cos(-B) = cos B (cos is even) and sin(-B) = - sin B (sin is odd). Similarly (7) comes from (6). (8) is obtained by dividing (6) by (4) and dividing top and bottom by cos A cos B, while (9) is obtained by dividing (7) by (5) and dividing top and bottom by cos A cos B. (10), (11), and (12) are special cases of (4), (6), and (8) obtained by putting A = B = .
Sum and product formulae
cos A + cos B = 2 cos A + B cos A - B
(13)
2
2
cos A - cos B = -2 sin A + B sin A - B
(14)
2
2
sin A + sin B = 2 sin A + B cos A - B
(15)
2
2
sin A - sin B = 2 cos A + B sin A - B
(16)
2
2
Note that (13) and (14) come from (4) and (5) (to get (13), use (4) to expand cos A =
cos(
A+B 2
+
A-B 2
)
and
(5)
to
expand
cos B
=
cos(
A+B 2
-
A-B 2
),
and
add
the
results).
Similarly (15) and (16) come from (6) and (7).
Thus you only need to remember (1), (4), and (6): the other identities can be
derived from these.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- math 113 hw 9 solutions
- trig key grosse pointe public school system gpps home
- exo7 exercices de mathématiques
- ap calculus bc 2009 scoring guidelines form b
- complex numbers and the complex exponential
- soluciones de los ejercicios del examen de cálculo del 29
- formulaire de trigonométrie circulaire
- euler s formula and trigonometry
- domain range and period of the three main trigonometric
- 2004 ap calculus ab scoring guidelines college board
Related searches
- log identities cheat sheet
- trig identities pdf
- integral identities pdf
- trig fundamental identities cheat sheet
- trig identities formula sheet pdf
- trigonometric identities cheat sheet pdf
- limits using trig identities calculator
- integral trig identities cheat sheet
- trig identities sin 2x
- trigonometric identities cheat sheet
- trig identities sin and cos
- trig identities chart