Practice!

Sample Problem

Given that t=-11π/6,

Evaluate sin t.

1/2

-√3/2

√3/2

-√2/2

Evaluate cos t.

1/2

-√3/2

√3/2

-√2/2

Evaluate tan t.

-1/√3

1/√3

-√3

√3

Evaluate csc t.

1/2

√3/2

-2

2

Evaluate sec t

-√3

2/√3

2

-1/2

Evaluate cot t.

√3

1/√3

1/2

-√3/2

Solution

Refer to the Unit Circle to find the (x, y) values of t=-11π/6:

Description: http://www.spsu.edu/math/edwards/1113/unit2.gif

Remember that -11π/6 is coterminal with (-11π/6+2π)=π/6.

The (x, y) values that correspond to t=π/6= (√3/2, 1/2)

sin π/6=y=1/2

cos π/6=x=√3/2

tan π/6=y/x=1/√3

csc π/6=1/y=1/(1/2)=2

sec π/6=1/x=1/(√3/2))=2/√3

cot π/6=x/y=(√3/2)/(1/2)=√3