Math 140

Class 10

Trigonometric Functions

Defined by “projecting” a point from the number circle to one of the axes.

• \(\cos t ={}\) the \(x\)-coordinate of the point \(t\) on the number circle.

• \(\sin t ={}\) the \(y\)-coordinate of the point \(t\) on the number circle.

Cosine and Sine

Basic Properties of Cosine

Basic Properties of Sine

Basic Properties of Cosine and Sine

Tangent and Cotangent

• \(\tan t ={}\) projection of \(t\) through the origin to the \(s\)-axis.

  Also the slope of the line through the origin and \(t\).

• \(\cot t ={}\) projection of \(t\) through the origin to the \(r\)-axis.

  Also the reciprocal slope of the line through the origin and \(t\).

Tangent

Basic Properties of Tangent

Cotangent

Basic Properties of Cotangent

Secant and Cosecant

Basic Properties of Secant and Cosecant