For the angle θ in a right-angled triangle as shown, the sides are usually name as follows:

• hypotenuse (the side opposite the right angle)
• adjacent (the side "next to" θ)
• opposite (the side furthest from the angle)

We can define the three trigonometrical ratios sine θ, cosine θ, and tangent θ as follows (usually written as sin θ, cos θ, and tan θ):

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

To make it easier to remember, many people use SOH CAH TOA, that is:

Sin θ = Opposite/Hypotenuse,

Cos θ = Adjacent/Hypotenuse, and

Tan θ = Opposite/Adjacent

SIGNS OF TRIGONOMETRIC FUNCTIONS

The Sign of the Trigonometric function depends on the quadrant that the angle is in.

• The sign is dependent on whether the opposite side or the adjacent side of the right triangle formed is positive or negative.
• The sign of the Sine and Cosecant function is determined by the sign of the opposite side.
• The sign of the Cosine and Secant function is determined by the sign of the adjacent side.
• The sign of the Tangent and Cotangent function is determined by the signs of the opposite and adjacent side. If they are different, then the Tangent function is negative. If they are the same, then the Tangent function is positive.
• The hypotenuse is always positive.

The signs in the table below are for angles that are within each quadrant border. They do not apply to the signs of the angles at the borders. Those are special as indicated earlier.

A table of signs is shown below:

Function	Quadrant 1	Quadrant 2	Quadrant 3	Quadrant 4
Sine and Cosecant	+	+	-	-
Cosine and Secan	+	-	-	+
Tangent and Cotangent	+	-	+	-