Mathematics · Grades 10–12
Trigonometry: identities and ratios
A focused reference to use alongside your practice.
Right-triangle ratios
These side-ratio definitions use an acute angle in a right triangle.
sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent
3–4–5 triangle: sin θ = 3/5, cos θ = 4/5, tan θ = 3/4
Fundamental identity
The identity holds for all real angles.
sin²θ + cos²θ = 1
(3/5)² + (4/5)² = 1
Tangent identity
Do not divide by zero at an angle where cosine is zero.
tan θ = sin θ/cos θ, cos θ ≠ 0
tan 45° = 1
Radian measure
For s = rθ, θ must be in radians.
180° = π radians; arc length s = rθ
r = 6, θ = π/3 → s = 2π
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.