Cosine rule

This proofs shows that the cosine rule is correct.

Distance formula between a point and a line

This proof shows a formula for calculating the distance between a point and a line in the form of y = ax + b.

Exact values of the trig functions

This table shows all exact values of sine, cosine and tangent.

Heron's formula: area of triangle

This shows Heron's formula for finding the area of any triangle.

The limit of sin(x) over x

This proof shows that the limit as x goes to zero of sin(x) over x converges to one.

Pythagorean theorem

This proofs shows how the famous Pythagorean theorem works: a^2 + b^2 = c^2

Sine rule

This proof shows that the ratio between a triangle's side length and the sine of its angle is the same for all sides.

Sine squared plus cosine squared is always one

This proof shows that sine squared plus cosine squared is always one, using the Pythagorean theorem.

Tangent is sine divided by cosine

This proof shows that sine divided by cosine is tangent.

Trig values of 15 degrees

This proof shows the exact value of sin(15), cos(15) and tan(15)

Trig values of 18 degrees

This proof shows the exact value of sin(18), cos(18) and tan(18)

Trig values of 3 degrees

This proof shows the exact value of sin(3), cos(3) and tan(3).

Trig values of 30 and 60 degrees

This proof shows the exact value of sin(30), cos(30), tan(30), sin(60), cos(60) and tan(60).

Trig values of 36 degrees

This proof shows the exact value of sin(36), cos(36) and tan(36)

Trig values of 45 degrees

This proof shows the exact value of sin(45), cos(45) and tan(45)

Trig values of 54 degrees

This proof shows the exact value of sin(54), cos(54) and tan(54)