Trigonometry Terms

Foundations 1

• TrigonometryTrigonometry is the branch of math that studies how the angles and the side lengths of triangles are related. Its three main ratios, sine, cosine and tangent, compare two sides of a right triangle. Knowing one side and one acute angle, or two sides, you can find every other side and angle without measuring them.Geometry, Algebra 2, Precalculus

Trigonometric ratios 5

• CosineCosine is the trigonometric ratio that compares the side adjacent to an angle with the hypotenuse of a right triangle: cos θ = adjacent/hypotenuse. On the unit circle, cos θ is the x-coordinate of the point at angle θ. The cosine of an angle equals the sine of its complement.Geometry, Algebra 2, Precalculus
• SecantSecant (sec) is the trigonometric function equal to 1 divided by cosine: sec θ = 1/(cos θ). In a right triangle it is the hypotenuse divided by the side adjacent to the angle. Secant is undefined wherever cosine is 0, such as at 90°, and its values are always at least 1 or at most −1.Algebra 2, Precalculus, Calculus
• SineSine is the trigonometric ratio that compares the side opposite an angle with the hypotenuse of a right triangle: sin θ = opposite/hypotenuse. On the unit circle, sin θ is the y-coordinate of the point at angle θ, so sine values always stay between −1 and 1.Geometry, Algebra 2, Precalculus
• SOH CAH TOASOH CAH TOA is a memory aid for the three basic trigonometric ratios in a right triangle: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent. Name the sides from the angle you are using, choose the ratio that links the sides you know and need, then solve.Geometry, Algebra 2, Precalculus
• TangentTangent (tan) is the trigonometric ratio of the side opposite an acute angle to the side adjacent to it in a right triangle: tan θ = opposite/adjacent. For legs 3 and 4, tan θ = 3/4 = 0.75. It is the TOA in SOH CAH TOA, and it equals (sin θ)/(cos θ).Geometry, Algebra 2, Precalculus

Vectors 1

• VectorA vector is a quantity that has both a size, called its magnitude, and a direction. It is drawn as an arrow from an initial point to a terminal point and written in components, such as v = ⟨ 4, 3 ⟩: 4 units right and 3 units up. Velocity and force are vectors; speed and mass are not.Precalculus

Unit circle and radians 2

• RadianA radian is a unit for measuring angles: one radian is the central angle that cuts off an arc exactly as long as the circle's radius. A full turn is 2π radians, so π radians = 180° and 1 radian is about 57.3°. To change degrees to radians, multiply by π/180.Geometry, Algebra 2, Precalculus
• Unit CircleThe unit circle is the circle with radius 1 centered at the origin, x^2 + y^2 = 1. An angle θ measured from the positive x-axis meets the circle at the point (cos θ, sin θ). This lets sine and cosine work for every angle, including obtuse and negative angles, not just the acute angles of right triangles.Algebra 2, Precalculus

Trig graphs 1

• PeriodThe period of a repeating function is the horizontal length of one complete cycle: the smallest distance after which the graph repeats exactly. y = sin x and y = cos x have period 2π, or 360°, and y = tan x has period π. For y = sin (Bx) or y = cos (Bx), the period is 2π/(|B|).Algebra 2, Precalculus

Identities and laws 2

• Law of CosinesThe law of cosines relates the three sides of any triangle to one of its angles: c^2 = a^2 + b^2 − 2ab cos C, where C is the angle across from side c. Use it to find the third side when you know two sides and the angle between them, or to find an angle when you know all three sides.Geometry, Algebra 2, Precalculus
• Law of SinesThe law of sines says that in any triangle, each side divided by the sine of its opposite angle gives the same number: a/(sin A) = b/(sin B) = c/(sin C). Use it to solve triangles that have no right angle when you know two angles and a side, or two sides and an angle opposite one of them.Geometry, Algebra 2, Precalculus

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Updated November 2026·Reviewed by the Effortless Math team