Thursday March 31, 2011

Today we jumped into the exciting new world of Chapter 5. Chapter 5 deals with Identities.

An identity function is defined as a function in which the domain values do not change at all. F(x)=x.

Today we learned a few of the many identities..

Reciprocal Identities

csc(x)= 1/sin(x) sec(x)=1/cos(x) cot(x)=1/tan(x) sin(x)=1/csc(x) tan(x)=1/cotan(x)

Quotient Identities

cotan(x)=cos(x)/sin(x)

Pythagorean Identities

sin²(x)+cos²(x)=1 tan²(x)+1=sec²(x) cotan(x)+1=csc²(x)

Even/Odd Identities

sin(-x)=-sine(x) csc(-x)=-csc(x) cos(-x)=cos(x) sec(-x)=sec(x) tan(-x)=-tan(x)

cotan(-x)=-cotan(x)

Co-Function Identities

sin(x)=cos(π/2-(x)) cos(x)=(pi/2-(x))

tan(x)=cotan(pi/2-(x))

sec(x)=csc(pi/2-(x))

csc(x)=sec(pi/2-(x))

cotan(x)=tan(pi/2-(x))