Pure Maths Formulae - Logs, Sequences, Trigonometry and Circles

When x = a^n, give an equation for n.

n = log a x for a > 0, x > 0

Give log a(x) + log a(y).

log a(x) + log a(y)= log a(xy)

Give log a(x) - log a(y)

log a(x) - log a(y) = log a(x/y)

Simplify log a(x^k)

log a(x^k) = k log a(x)

Give an equation for the nth term of an arithmetic sequence.

un = u1 + (n - 1)d

Give the equation for the nth term of a geometric sequence.

un = ar^(n-1)

If sin² x + cos² x = 1, give equations for sec² x and cosec² x.

sec² x = 1 + tan² x

cosec² x = 1 + cot² x

Give the double angle formula for sine.

sin 2A = 2 sin A cos A

Give the double angle formula for cosine.

cos 2A = cos² A - sin² A = 2cos² A - 1 = 1 - 2sin² A

Give the double angle formula for tangent.

tan 2A = 2tan A / (1 - tan² A)

Give the equation of an arc length.

s = rΘ

s = arc length, r = radius, Θ = angle in radians.

Give the area of a sector of a circle.

A = ½ r² Θ

A = area of a sector, r = radius, Θ = angle in radians