Phoenix ED [Basics of Trigonometry] 9831333221 Page 1 y = tan x y

Phoenix ED
y = tan x
9831333221
[Basics of Trigonometry]
y = ( cos x , sin x )
Page 1
Phoenix ED
[Basics of Trigonometry]
θ (deg)
θ (rad)
sin(θ)
cos(θ)
tan(θ)
cot(θ)
sec(θ)
cosec(θ)
0o
0
0
1
0
undefined
1
undefined
П
12
√3 − 1
√3 + 1
√3 − 1
√3 + 1
2√2
2√2
10 + 2√5
4
√5 − 1
ඥ 10 + 2√5
15 o
18 o
22.5 o
30 o
36 o
45 o
54 o
60 o
67.5 o
72 o
75 o
9831333221
2√2
П
10
П
8
√5 − 1
4
ඨ
П
6
П
5
ඨ
П
4
3П
10
2П
5
5П
12
2√2
1
2
ඨ
ඨ
√2 + 1
2√2
10 + 2√5
4
√3 + 1
2√2
√2 + 1
2√2
√3
2
√5 + 1
4
√2
2
√3
2
ඨ
ඨ
10 − 2√5
4
√5 + 1
4
П
3
3П
8
√2 − 1
2√2
√2
2
ඨ
10 − 2√5
4
1
2
ඨ
√2 − 1
2√2
√3 + 1
ඥ 10 + 2√5
ඨ
√2 − 1
√2 + 1
√3
3
ඥ 10 − 2√5
√3 − 1
√5 − 1
ඨ
√2 + 1
√2 − 1
1
1
√5 + 1
ඥ 10 − 2√5
√3
√3
3
√2 + 1
√2 − 1
10 + 2√5
√5 − 1
√5 + 1
ඨ
√2 − 1
√2 + 1
√5 − 1
ඨ
2√2
√2 + 1
2√3
3
4
√5 + 1
ඨ
2√2
√2 − 1
4
√5 − 1
ඥ 10 + 2√5
√5 − 1
2√2
√3 − 1
√3 + 1
√3 − 1
√3 − 1
ඨ
2√2
Page 2
√2 − 1
4
10 − 2√5
√2
4
√5 + 1
2√3
3
2
ඨ
2√2
2
4
10 − 2√5
ඥ 10 + 2√5
√3 + 1
ඨ
√2
√5 − 1
4
√3 − 1
4
4
ඨ
√5 + 1
ඥ 10 − 2√5
ඨ
√3 − 1
√3
√5 + 1
ඥ 10 − 2√5
√3 + 1
ඨ
ඨ
2√2
√2 + 1
4
10 + 2√5
2√2
√3 + 1
Phoenix ED
90 o
120
o
135 o
150
o
180 o
210 o
225 o
240 o
270 o
300 o
315 o
330 o
360 o
9831333221
П
2
2П
3
3П
4
5П
6
[Basics of Trigonometry]
1
√3
2
√2
2
1
2
0
П
7П
6
5П
4
−
−
4П
3
−
5П
3
−
3П
2
7П
4
11П
6
2П
0
1
2
√2
2
√3
2
−
−
−
1
2
√2
2
√3
2
undefined
−√3
-1
−
-1
−
−
√3
2
√2
2
−
1
2
√3
3
1
1
√3
√3
3
0
0
1
-1
−
√3
3
0
−
√3
3
-1
1
2√3
3
√2
2√3
3
2√3
3
−√3
√3
2
−
√3
1
2
1
2
−√3
−√2
√3
3
√3
2
−
-1
-2
-1
undefined
√2
2
√3
3
undefined
0
√2
2
−
undefined
0
-1
−
0
−√2
-2
2
undefined
-2
−√2
−
undefined
2
√2
−√3
2√3
3
undefined
1
Page 3
2√3
3
-1
−
2√3
3
−√2
-2
undefined
Phoenix ED
[Basics of Trigonometry]
Degree/Radian Relationship: 180° = π radians
Sum and Difference Identities:
Allied Angles
cos(−x)
=
cos(x)
sin(A + B)
=
sinA . cosB + cosA . sinB
sin(−x)
=
−sin(x)
sin(A − B)
=
sinA . cosB − cosA . sinB
tan(−x)
=
−tan(x)
cos(A + B)
=
cosA . cosB − sinA . sinB
cos(90 − θ)
=
sin(θ)
cos(A − B)
=
cosA . cosB + sinA . sinB
sin(90 − θ)
=
cos(θ)
tan(A + B)
=
tan(90 − θ)
=
cot(θ)
cot(90 − θ)
=
tan(θ)
sec(90 − θ)
=
cosec(θ)
cosec(90 − θ)
=
sec(θ)
tanA + tanB
1 − tanA . tanB
tan(A - B)
=
tanA - tanB
1 + tanA . tanB
cot(A + B)
=
cotA cotB - 1
cot(A - B)
=
cotA cotB + 1
cotA + cot B
cot B - cot A
Double-Angle Identities:
cos(2A)
Triple-Angle Identities:
=
cos2 A − sin2 A
cos(3A)
=
4cos3 A − 3cos A
=
1 − 2 sin2 A
sin(3A)
=
3sinA - 4 sin3A
=
2
tan(3A)
=
3tanA –tan3A
=
2 cos A – 1
2
1 − 3 tan2 A
1 − tan A
2
1 + tan A
sin(2A)
=
2 sinA cosA = 2 . tanA
1 + tan2 A
tan(2A)
=
2 . tanA
1 − tan2 A
Half-Angle Identities:
cos(A)
Product-to-Sum Identities:
2
2
=
cos (A/2) − sin (A/2)
2cosAcosB
=
[cos (A + B) + cos (A − B)]
=
1 − 2 sin2 (A/2)
2sinA sinB
=
[cos (A − B) − cos (A + B)]
=
2 cos2 (A/2) − 1
2sinAcosB
=
[sin (A + B) + sin (A − B)]
sin(A)
=
2 sin(A/2) . cos(A/2)
2cosAsinB
=
[sin (A + B) – sin (A − B)]
tan(A)
=
2 . tan(A/2)
1 − tan2 (A/2)
Sum-to-Product Identities:
sinA+sinB
=
2 sin (A + B) cos(A - B)
sinA−sinB
=
2 cos (A + B) sin(A - B)
cosA+cosB
=
2 cos (A + B) cos(A - B)
cosA−cosB
=
− 2 sin(A + B) sin(A - B)
2
2
2
2
2
9831333221
2
Important Formulae
Sin (A+B) . Sin (A-B)
=
Sin2A – Sin2B
Cos (A+B) . Cos (A-B)
=
Cos2A – Sin2B
2
2
Page 4