sin2A=?
2sinAcosA
cos2A=?
cos squaredA- sin squared A
2cos squared A-1
1-2sin squared A
tan2A=?
2tanA/1-tan squared A
what is acute?
0-90 degrees
what trigs are positive when the angle is acute?
sin cos and tan
what is obtuse?
90-180 degrees
what trigs are positive when the angle is obtuse?
only sin
what is reflex?
180 or more degrees
what is the derivative of lnf(x)?
f’(x)/f(x)
what is the integral of sinx?
-cosx
what is the integral of sin(ax+b)?
-1/a cos(ax+b)
what is the integral of cos(x)?
sinx
what is the integral of cos(ax+b)?
1/a sin(ax+b)
what is the integral of e^x?
e^x
what is the integral of e^ax+b?
1/a e^ax+b
what is the integral of 1/x?
ln x
what is the integral of 1/ax+b?
1/a ln(ax+b)
when integrating by substitution how do you choose which part to be u?
Logarithmic
Algebraic
Trigonometric
Exponential
circle circumference=?
2πr
arc length=?
rθ
arc area=?
1/2 r squared θ
in small angle approximations, sinx=?
x
in small angle approximations, cosx=?
1-1/2 x squared
in small angle approximations, tanx=?
x
what is an arithmetic sequence?
when the difference between 1 term and the next is always the same
what is a geometric sequence?
when the ratio of 1 term to the next is always the same.
what is a periodic sequence?
it repeats itself at regular intervals
what is a series?
the sum of terms in a sequence.
what is a deductive definition?
gives a direct formula for the kth term of the sequence in terms of k.
what is an inductive definition?
tells you how to find a term in the sequence from the previous term, the definition must also include the first term of the sequence.
what range is the normal binomial expansion valid for?
-1
WHEN PROVING SIN X HAS NO REAL SOLUTIONS SAY…
SIN X IS ONLY DEFINED FOR -1
If each term in the binomial expansion is positive what does that mean?
The estimated value (based on not all the terms eg up to x awaited) is an underestimate- bc increasing no of terms increases result.
WHEN IT SAYS SET OF VALUES WHAT DO U DO
WRITE IT IN SET NOTATION
WHEN USING ALGEBRA TO SOLVE A PROBLEM REMEMBER TO
DEFINE UR VARIABLES!!