Pure Flashcards
How to transform logarithmic graphs?
Write as a familiar function y=f(x) and then use normal transformation rules.
Relationship between lines of lnx and e^x
Reflection of each other in the line y=x
What does y=e^x look like?
Acceleration, crosses y-axis at (0,1), asymptotes of y=x and x-axis
What does y=lnx look like?
Deceleration, crossing x-axis at (1,0), asymptotes of y=x and y-axis
How to convert a circle’s equation?
Complete the square
Which formula to use when r>1?
r^n - 1, r-1 instead of the other one (on formula sheet)
sin2A
2sinAcosA
cos2A
cos^2A - sin^2A, 1-2sin^2A, 2cos^2A -1
tan2A
2tanA/1-tan^2A
sec^2A
1+tan^2A
cosec^2A
1+cot^2A
How to write parametric equations as a function?
x = p(t), y = q(t)
What is the domain of f(x)?
range of x
What is the range of f(x)?
range of y
How to draw functions as graphs?
Work out domain and range.
domain of secx?
R except even multiples of pi/2
range of secx?
-1≤ or ≥1
domain of cotx?
R, except multiples of π
range of cotx?
R
range of cosec?
-1≤ or ≥1
domain of cosec?
R, except multiples of π
domain of arcsinx
-1 ≤ x ≤ 1
range of arcsinx
[-π/2, π/2]
domain of arccosx?
-1 ≤ x ≤ 1
range of arccosx?
[0, π]
how to draw arcfunctionx?
restrict domain of ‘normal’ function, then reflect in y=x
domain of arctanx?
all real numbers
range of arctanx?
[-π/2, π/2]
cos(-A) is the same as
cos(A)
sin(-A) is the same as
-sin(A)
sin30
1/2
cos30
√3/2
tan30
√3/3
sin45
√2/2
cos45
√2/2
tan45
1
sin60
√3/2
cos60
1/2
tan60
√3
cosine rule
a² = b² + c² - 2bccosA
How can we use the discriminant?
It’s value tells us the number of times two lines intersect.
when modelling parametric, what is the value of dy/dt at max/min?
0, like dy/dx is 0
