Pure Maths

Arc Length

rTheta

Sector Area

(1/2)r²theta

Segment Area

(1/2)r²(θ - sin(θ))

Domain

x values in f(x)

Range

y values in f(x)

Arithmetic nth term

u_{n = a+(n-1)d}

Geometric nth term

u_n = ar^n-1

sin2theta

2sinthetacostheta

cos2theta

cos²theta - sin²theta = 2cos²theta-1 = 1-2sin²theta

tan2theta

(2tantheta)/(1-tan^²theta)

implicit differentiation

f’(x) * dy/dx

integrate 1/x

ln|x| + c

integrate secxtanx

secx + c

integrate cosec²x

-cotx + c

integrate cosecxcotx

-cosec x + c

parametric integration

y dx/dt, change limits