formula of exterior angles of regular polygons
360 / n
n = no. sides
formula of interior angles of regular polygons
180 ( n -2 )
n = no. sides
Perimeter of circle (circumference)
πd
Area of circle
πr^2
Area of trap.
h( a+b )/ 2
a & b are parrel sides
Area of curved surface area of cone
πrL
L = length from bottom to tip
Area of surface of Sphere
4πr^2
volume of pyramid
1/3 x base area x perpendicular height
Volume of cone
1/3 x πr^2 h
Volume of Sphere
4/3 x πr^3
formula for arithmetic sequence
a n = a1 + (n-1 )d
a n = nth term
a1 = first term
d = diff btw terms
formula for geometric sequence
a n = a1 x r^n-1
a n = nth term
a1 = first term
r = ratio
formula for gradient of straight line
-rise/ run
-without graph: need 2 points
y2 - y1/ x2 - x1
-always make fraction
formula for y-intercept/ equation of straight line
-need 1 point & gradient
y - y1 = m (x - x1)
formula for midpoint of straight line
- x1 + x2/ 2 (for x)
- y1 + y2/ 2 (for y)
- (x, y)
formula for length of straight line
-use Pythagoras
-√ (x2 - x1)^2 + (y2 - y1)^2
formula for Pythagoras
-a^2 + b^2 = c^2
-only in right angel triangles
Quadratic formula
2a -put bracket in calc when (b)^2
how to find θ for right angled triangles
-SOH CAH TOA
sin θ = O/ H
cos θ = A/ H
tan θ = O/ A
-O is side opposite θ
-H is longest side
functions for sine, cosine, tan
1) sine
x< 180 (x = +) __ sin x = sin (180 - x)
x> 180 (x = -) __ x - 180 = y , sin x = sin (360- y)
2) cosine
x< 90/ x> 270 (x = +) __ cos x = -cos (180 - x)
90< x< 270 (x = -) __ cos x = cos (360 - x)
3) tan
tan x = tan (180 + x)
sine rule
A, B, C - angle
a, b, c - side (side has to be opposite same letter angle)
a b
——– = ——–
sin A sin B
-cross multiply
-2 sides, 1 angle/ 1 side, 2 angles
area of non right angle triangle
1/2 x ab sincC
cosine rule
A, B, C - angle
a, b, c - side (side has to be opposite same letter angle)
-c^2 = a^2 + b^2 - 2ab cos C
-cos C = a^2 + b^2 - c^2
————————-
2ab
-3 sides/ 2 sides, 1 angle
how to find length & angle for 3D triangle in a square/ rectangle
length:
-find hypothenuse of base
-find hypothenuse of 3D triangle
angle:
-SOH CAH TOA with values
