Download Trig Formulas Super Summary Sheet

MCV4U Calculus & Vectors
Trigonometric Formulas Super Summary Sheet
Trig. Ratios of Special Angles
0
π
π
π
3
6
4
2π
sin
1
2
2
2
3
2
cos
3
2
2
2
1
2
tan
3
3
1
30o
45o
0
π
1
0
3π
2
-1
CAST rules
sin x
lim
=1
x→ 0
x
π−ϑ
π
+θ
2
sin mx
sin mx m
lim
= lim
=
x→ 0
x
→
0
nx
sin nx
n
0
-1
0
0
NA
0
NA
lim cos x = 1
180o 270o
lim tan x = 0
60o 0o/360o 90o
d (sin x)
= cos x
dx
d (cos x )
= − sin x
dx
d (tan x )
= sec 2 x
dx
tan x + tan y
1 − tan x tan y
tan x − tan y
tan( x − y ) =
1 + tan x tan y
x
= ±
2
1 − cos x
1 + cos x
2π − ϑ
3π
+θ
2
y = tan x
D: x ≠ (2 n
R: y ∈ R
Period = π
VA: x = (2 n
n∈ I
+ 1 )π
2
+ 1 )π
2
Double Angle formulas
sin 2 x = 2 sin x cos x
cos 2 x = cos
2
= 2 cos
x − sin
2
2π − ϑ
3π
+θ
2
2
x
tan 2 x =
2 tan x
1 − tan 2 x
x −1
= 1 − 2 sin
o
sin θ =
h
a
cos( a − b ) − cos( a + b )
sin a sin b =
2
cos( a + b ) + cos( a − b )
cos a cos b =
2
cos( a − b ) − cos( a + b )
tan a tan b =
cos( a + b ) + cos( a − b )
y = cos x
D: x ∈ R
R : -1 ≤ y ≤1
Period = 2π
RHHS Mathematics Department
C
2
x
Trigonometric Ratios (Soh Cah Toa)
Half Angle Formulas (Optional) Product Angle Formulas (Optional)
tan
T
x→ 0
tan( x + y ) =
x
1 + cos x
=±
2
2
A
ϑ
π
−θ
2
Reciprocal Identities Quotient Identities Pythagorean Identities
1
sin 2 θ + cos 2 θ = 1
sin θ
d (csc x )
csc
θ
=
tan θ =
= − csc x cot x
sin θ
cos θ
sin 2 θ = 1 − cos 2 θ
dx
1
cos θ
d (sec x )
sec θ =
cos 2 θ = 1 − sin 2 θ
= sec x tan x
cot θ =
cos
θ
dx
sin θ
1 + tan 2 θ = sec 2 θ
1
d (cot x )
cot θ =
= − csc 2 x
1 + cot 2 θ = csc 2 θ
tan θ
dx
sin( x + y ) = sin x cos y + cos x sin y
sin( x − y ) = sin x cos y − cos x sin y
cos( x + y ) = cos x cos y − sin x sin y
cos( x − y ) = cos x cos y + sin x sin y
cos
S
x→ 0
Addition & Subtraction Formulas
x
1 − cos x
sin
=±
2
2
π
2
0 / 2π
π+ϑ
3π
−θ
2
x→ 0
1
∂ & θ are acute angles
π
cos x − 1
=0
x
lim sin x = 0
lim
x→ 0
3
Derivative Rules of Trig
y = sin x
D: x ∈ R
R : -1 ≤ y ≤1
Period = 2π
Date:
Limits of Trig
π
2
Page 1 of 1
θ
cos θ =
opp
hyp
adj
hyp
tan θ =
Sine Law
opp
adj
A
sin A sin B sin C
=
=
a
b
c
Cosine Law
c
b
a 2 = b 2 + c 2 − 2 bc cos A
b 2 = a 2 + c 2 − 2 ac cos B
c 2 = a 2 + b 2 − 2 ab cos C
y = csc x
D : x ≠ nπ
R : y ≤ -1 or y ≥ 1
Period = 2π
VA : x = nπ
n∈I
y = sec x
D : x ≠ (2 n
B
a
y = cot x
D : x ≠ nπ
R : y∈R
R : y ≤ -1 or y ≥ 1
Period = π
Period = 2π
VA : x = nπ
VA: x = (2 n + 1 )π
n∈I
2
n∈I
+ 1 )π
2
C