Malorie's blog

8.4 relationships among the functions

In order to do this, you must know the following:

(Reciprocal Relationships)
csc theta= 1/sin theta
sec theta= 1/cos theta
cot theta= 1/tan theta

(Relationships with Negatives)
sin(-theta)=-sin theta and cos(-theta)= cos theta
csc(-theta)=-csc theta and sec(-theta)= sec theta
tan(-theta)=-tan theta and cot(-theta)=-cot theta

(Pythagorean Relationships)
sin^2 theta+cos^2 theta= 1
1+tan^2 theta= sec^2
1+cot^2 theta^2theta

(Cofunction Relationships)
sin theta= cos (90 degrees-theta) and cos theta=sin (90 degrees-theta)
tan theta= cot(90 degrees-theta) and cot theta=tan(90 degrees- theta)
sec theta=csc(90 degrees-theta) and csc theta= sec(90 degrees-theta)

In order to do this you must also follow these steps:

Step 1) look for Pythagorean identities

Step 2) Move everything to sin and cos or tan if possible

Step 3)Use algebra to simplify

Step 4)Look for identities again

Step 5)Use algebra (combining, dividing, factoring, and foiling fractions)


Example :

1-Sin^2 theta/ tan^2

1- sin^2 theta/ 1/ sin^2 theta/ cos^2 theta = 1- cos^2 theta(sin^2theta)/ sin^2 theta

1-cos^2 theta= sin^2 theta

Final answer= sin^2 theta