Checkpoint Flashcards
dawad
Sin^2(x) + cos^2(x) =?
1
1 + tan^2(x) =?
sec^2(x)
Sin(2x) =?
2sin(x)cos(x)
1 + cot^2(x) =?
csc^2(x)
Cos(2x) =?
2cos^2(x) - 1
SinACosB =?
[sin(A - B) + sin(A + B)] / 2
SinAsinB =?
[cos(a-b) - cos(A + B)] / 2
CosACosB = ?
[cos(A - B) + cos (A + B)]/2
Derivative of sinx?
cosx
Derivative of cosx?
-sinx
Derivative of tanx?
sec^2(x)
Derivative of secx?
secxtanx
derivitive of cscx?
-Cscxcotx
Antiderivitive of cosx?
Sin(x) + C
derivitive of cotx?
-csc^2(x)
Antiderivitive of sinx?
-Cosx + C
Antiderivitive of tanx?
Ln|secx| + c
Antiderivitive of secx?
Ln|secx + tanx| + c
Antiderivitive of cscx?
-Ln|cscx + cotx| + C
Antiderivitive of cot?
Ln|sinx| + c
Antiderivitive of sec^2(x)
Tanx + C
Antiderivitive of csc^2(x)
-cotx
Antiderivitive of secxtanx
secx
Antiderivitive of cscxcotx
-Csc(x)
Sin^m times cos^n
If n odd: substitute u = sinx, du = cosx. Leave an even power of cosine
If m odd: substitute u = cosx, du = -sinx. Leave an even power of sine.
If both even revert to odd
Tan^m times sec^n
If n even: substitute u = tanx and du = sec^2(x). Use trig identity 1 + tan^2 = sec^2(x)
if m odd: substitute u = secx and du = secxtanx. Use the trig identities to convert the remaining factors in terms of secxtan^2(x) = sec^2(x) - 1 = u^2 - 1
a^2 + x^2 =
X = atan0
a^2 - x^2 =
X = asin0
x^2 - a^2 =
X = asec0
