Trigonometry Flashcards
1
Q
sin30
A
1/2
2
Q
cos30
A
root3/2
3
Q
tan30
A
1/root3
4
Q
sin45
A
1/root2
5
Q
cos45
A
1/root2
6
Q
tan45
A
1
7
Q
sin60
A
root3/2
8
Q
cos60
A
1/2
9
Q
tan60
A
root3
10
Q
tanx
A
sinx/cosx
11
Q
cotx
A
cosx/sinx
12
Q
sin^2x+cos^2
A
=1
13
Q
1+cot^2
A
=cosec^2x
14
Q
1+tan^2x
A
=sec^2x
15
Q
cosine rule
A
c^2 = a^2 + b^2 − 2ab cos(C)
cos(c) =( a^2 + b^2 −c^2) / 2ab
16
Q
angle size (radians)
A
arc length / radius
17
Q
area of a sector
A
r^2 theta /2
18
Q
area of minor segment
A
r^2/2 (theta - sintheta)
19
Q
small angles
A
sinx ~x
tanx~ x
cosx ~ 1
20
Q
ambiguous case sine rule
A
if (180 - angle) + given angle < 180
21
Q
differentiating trig
A
f'(sinx) = cosx f'(cosx) = - sinx f'(tanx) = sec^2x f'(secx) = secxtanx f'(cosecx) = -cosecxcotx f'(cotx) = - cosec^2x
22
Q
integrating trig
A
sin x dx = − cos x + C cos x dx = sin x + C tan x dx = − ln |cos x |+ C sec^2x dx = tan x + C cosec^2x dx = − cot x + C cosecx cotx = -cosecx
23
Q
cos2x
A
cos^2x - sin^2x
2cos^2x-1
1-2sin^2x
24
Q
sin2x
A
2sinxcosx
25
Q
sec^2x
A
1+tan^2x
26
Q
cosec^2x
A
1+cot^2
27
Q
cos^2x-sin^x
A
cos2x
28
Q
2cos^2x-1
A
cos2x
29
Q
1-2sin^2x
A
cos2x
30
Q
2sinxcosx
A
sin2x
