Ximpledu

Trigonometry (Right Triangle)

See how to find the trigonometric ratios in a right triangle
(sine, cosine, tangent, cosecant, secant, cotangent).
12 examples and their solutions.

Sine

Formula


sin θ = (opposite side)(hypotenuse)
SOH: Sine, Opposite side, Hypotenuse

Example

sin θ = ?

Solution

Example

sin θ = ?

Solution

Example

sin θ = 45, x = ?

Solution

Cosine

Formula


cos θ = (adjacent side)(hypotenuse)
CAH: Cosine, Adjacent Side, Hypotenuse

Example

cos θ = ?

Solution

Example

cos θ = ?

Solution

Example

cos θ = 35, x = ?

Solution

Tangent

Formula


tan θ = (opposite side)(adjacent side)
TOA: Tangent, Opposite side, Adjacent Side

Meaning

Tangent means the slope: y/x.

Example

tan θ = ?

Solution

Example

tan θ = ?

Solution

Example

tan θ = 76, x = ?

Solution

Cosecant

Formula


csc θ = 1sin θ
= 1(opposite side)(hypotenuse)
Sine

Example

csc θ = ?

Solution

Secant

Formula


sec θ = 1cos θ
= 1(adjacent side)(hypotenuse)
Cosine

Example

sec θ = ?

Solution

Cotangent

Formula


cot θ = 1tan θ
= 1(opposite side)(adjacent side)
Tangent

Example

cot θ = ?

Solution