Pure Maths Flashcards
Pythagorean triples
4,3. 5
12,5. 13
24,7. 25
15,8. 17
Sin(A)=
Cos(90-A)
Tan θ
sin θ / cos θ
Sec x
1/cos x
Cosec x
1/sin x
Cot x
1 / tan x = cos x / sin x = cosec x / sec x
Y = sec θ (graph)
- symmetry in y-axis
- has period 360
- Asymptotes of -90, 90, 270
Y = sec θ (graph domain and range)
- domain x∈R, x≠90, 270, 450
- range y ≤-1 or y≥1
Y = cosec θ (graph)
- has period 360
- vertical asymptotes for which sin x = 0 (180, 360)
Y = cosec θ (graph domain and range)
- domain x∈R, x ≠ 0, 180, 360
- range y ≤-1 or y≥1
Y = cot θ (graph)
- has period 180
- vertical asymptotes for which tan x = 0 (0, 180, 360
Y = cot θ (graph domain and range)
- domain x∈R, x ≠ 0, 180, 360
- range y∈R,
Sec^2x
1 + tan^2 x
Cosec^2x
1 + cot^2x
Arcsin x (domain and range)
Domain -1≤ x ≤ 1
Range -90 ≤ arcsinx ≤ 90
Arccos x (domain and range)
Domain -1≤ x ≤ 1
Range 0 ≤ arccos x ≤ 180
Arctan x (domain and range)
Domain x∈R
Range -90 ≤ arctan x ≤ 90
Un (arithmetic)
A + (n-1) d
Sn (arithmetic)
N/2 (2a + (n-1) d)
Un (geometric)
Ar^(n-1)
Sn (geometric)
(A (r^(n-1)))/r-1
Sum to infinity ∞
A/1-r
|r| < 1
V=ab^t
A= initial value
B= the annual proportional decrease (-ve)/increase (+ve) in the value of the car
Y=log 9 (x+a)
(0, log 9 (x+a)) (-a+1, 0)