# Shared Flashcard Set

## Details

Definitions: Trig Functions
Definitions of sin, cos, tan, sec, csc, cot
6
Mathematics
08/08/2020

Term

Identify sine on the unit circle.

 sin(θ) [image]
Definition
 y = opposite hypotenuse

The sine is the ratio of the length opposite angle θ divided by the hypotenuse. For the unit circle this corresponds to y/1 = y.

Term

Identify cosine on the unit circle.

 cos(θ) [image]
Definition

The cosine is the ratio of the length adjacent angle θ divided by the hypotenuse. For the unit circle this corresponds to x/1 = x.

Term

Identify tangent on the unit circle.

 tan(θ) [image]
Definition
 x = sin(θ) = opposite y cos(θ) adjacent

The tangent is the ratio of the lengths opposite and adjacent to angle θ. For the unit circle this corresponds to y/x.

Term

Identify cotangent on the unit circle.

 cot(θ) [image]
Definition
 y = cos(θ) = 1 = adj. x sin(θ) tan(θ) opp.

The cotangent is the ratio of the lengths adjacent to and opposite angle θ, or 1/tan. For the unit circle this corresponds to x/y.

Term

Identify secant on the unit circle.

 sec(θ) [image]
Definition
 1 = 1 = hypotenuse x cos(θ) adjacent

The secant is the hypotenuse length divided by the length adjacent the angle θ, or 1/cos. For the unit circle this corresponds to 1/x.

Term

Identify cosecant on the unit circle.

 csc(θ) [image]
Definition
 1 = 1 = hypotenuse y sin(θ) opposite

The cosecant is the hypotenuse length divided by the length adjacent the angle θ, or 1/sin. For the unit circle this corresponds to 1/y.

Supporting users have an ad free experience!