Practice!

Sample Problem

The terminal side of θ lies on the line 2x-3y=0; θ lies in Quadrant III. Find:

sin θ=

-2/√13

-3/√13

-2/3

-√13/2

cos θ=

-2/√13

-1

 -3/√13

√13/3

tan θ=

3/2

2/3

-2/3

-2/√13

sec θ=

√13/2

-√13/2

-√13/3

√13/3

csc θ=

√13/2

-√13/3

√13/3

-√13/2

cot θ=

3/2

-3/2

2/3

-2/3

Solution

Take the point (-1, -2/3) which is in Quadrant III and on the line 2x-3y=0.

R=== =√13/3

Sin θ=y/r=(-2/3)/(√13/3)=-2/√13

Cos θ=x/r= (-1)/(√13/3)=-3/√13

Tan θ=y/x=(-2/3)/(-1)=2/3

Sec θ=1/cos θ=-√13/3

Csc θ=1/sin θ=-√13/2

Cot θ=1/tan θ=3/2