Practice!

Sample Problem

Evaluate sin 2u, cos 2u, and tan 2u if cot u=√3, π<u<3π/2.

1)Sin 2u=

1/2

-√3/2

√3/2

√2/2

2)Cos 2u=

1/2

-1/2

√3/2

-√2/2

3)Tan 2u=

1/√3

-1/√2

-√3

√3

Solution

Cos u=√3=cos u/sin u=√3 , cos u=√3 sin u

Cos2u+sin2u=1 , 3sin2u+sin2u=1

4sin2u=1 , sin2u=1/4

Sin u=-1/2 (since we know u is in Quadrant III)

Cos u=√3, sin u=√3 *(-1/2)=-√3/2

Cos u=√3 , tan u=1/√3

1)Sin 2u=2sinucosu=2(-1/2)(-√3/2)=√3/2

2)Cos 2u=1-2sin2u=1-2(-1/2)2=1-2(1/4)=1/2

3)Tan 2u=