Trigonometry and Differentiation Flashcards
What are the 4 complementary relationship formulas?
sin(Π/2- θ)=cos θ
cos(Π/2- θ)=sin θ
sin(Π/2+ θ)=cos θ
cos(Π/2+ θ)= -sin θ
What are the starting y-points for sin graphs and cos graphs?
sin: 0
cos: 1
What are the symmetrical properties (due to odd/even functions) of sin (-θ), cos(-θ) and tan(-θ)?
-sinθ
cosθ
-tanθ
What are the 3 techniques to consider when dealing with trig equations containing more than one trig equation?
- any common factors which will enable us to factorise?
- any squared signs so we can use sin^2x + cos^2x =1
- is sinx/cosx= tanx helpful?
How to find average rate of change for an interval and instantaneous rate of change at a point?
av rate of change: y2-y1/ x2-x1
instant: f’(x)
What are the 3 methods of determining the nature of a stationary point?
- Calculate y-coords of points slightly to the left and slightly to the right
- calculate gradient at points slightly to the left and right
- use second derivative
Describe what these become on a derivative graph:
stationary point of inflection
non-stationary points of inflection
turning point
what abt gradient?
- stationary point on the x axis
- stationary point not on the x axis
- x axis
hv positive gradient= derivative graph above x axis
hv negative gradient= derivative graph below x axis
How to use derivatives to determine velocity and acceleration displacement?
Displacement–dif–> velocity –dif–> acceleration
What is the derivative of: a(x^n)
an(x^n-1)
What is the derivative of: e^kx
ke^kx
What is the derivative of: e^f(x)
f’(x) e^f(x)
What is the derivative of: k ln x
k/x
What is the derivative of: ln kx
1/x
What is the derivative of: ln f(x)
f’(x)/ f(x)
What is the derivative of: sin kx
k cos kx
What is the derivative of: sin f(x)
f’(x) cos f(x)
What is the derivative of: cos kx
-k sin kx
What is the derivative of: cos f(x)
- f’(x) sin f(x)
What is the derivative of: tan kx
k/ cos^2kx
What is the derivative of: tan f(x)
f’(x)/ cos^2 f(x)
(f(x))^n
n (f(x))^n-1 f’(x)
What is the formula for surface area of a cylinder?
2πr^2 + 2πrh
What is the formula for surface area of a cone?
πrs+ πr^2
What is the formula for volume of a cylinder?
πr^2h
What is the formula for volume of a cone?
1/3hπr^2
