C4 Flashcards
How would a partial factor which has a (x-1)(x^2+4) denominatior be written ?
A/(x-1) + (Bx-c)/(x^2+4)
If when doing the general binomial expansion and the constant is not 1 how can it be written?
(a+b)^n = a^n × (1+(b÷a))^n
What is cosec
1÷ sin
What is sec
1÷cos
What is cot
1÷tan
What are the inverse trig identities to know?
Tan^2 +1 = sec^2
Cot^2+1=cosec^2
Sin2x=
2sinxcosx
What does cos(2x) equal
Cos^2 -sin^2
1-2sin^2
2cos^2 -1
How would you write sin(75) in surd form
write is as sin(30+45), then expand and simplify.
write 5cosσ-12sinσ in the form Rcos(σ+θ)
R(cosσcosθ-sinσsinθ) Rcosθ=5 Rsinθ=12 θ=67.4 R=the root of 5^2 plus 12^2 which is 13 13cos(θ+67.4)
How do you differentiate a parametric equation?
Differentiate the different parts and use the chain rule to find dy/dx.
It is usually the differential of y divided by the differential of x.
what is the formula for the volume of revolution around the x axis?
intergrate pi*(y^2) for x axis
Use pi*(x^2) for the y axis.
in the formula booklet for the plane going through a point, what does the a and n mean?
a is a point that is on the plane. n is a normal to the plane.
the coefficeints of the plane are the values of the perpendicular.
how can you tell that two planes are parallel?
The coefficients will be the same.
how do you find the angle between 2 vectors?
cos theta = (a dot b) / |a||b|
what does the cross product give?
a vector that is perpendicular to 2 different vectors.
What is the parametric equation of a circle?
X= a+rcos⊝
Y= b+rsin⊝
r is the radius and the centre is (a,b)
How would the fraction with denominatior (x-1)(x+2)² be written in partial fractions?
A/(x-1) + B/(x+2) + C/(x+2)²
For what values of x are binomial expansions valid?
For (1+x)ª |x|
What is a vector perpendicular to a plane?
One with the same coefficients of the plane.
How do you find the angle between two planes?
Angle between the normals
