Suppose sin ß=(1/3) where (π/2) <= ß<=π and cos ø =(4/5) where ((3π)/2)<=ø<=2π?

Question

**Note: π = pi; ß and ø are variables 

Find

1) tan ß 
2) sin ø 
3) sin(2ß) 
4) cos(2ø)

Answer 1

The functions are , and where .

(1) Find .

Step 1:

.

Pythagorean identity: .

, lies in the second quadrant.

Therefore, is negative.

.

Substitute in the above expression.

.

Step 2:

.

Substitute   and  in the above expression.

Solution:

.

Answer 2

(2)

Find .

 where .

Pythagorean identity: .

.

 

As , then  lies in fourth quadrant.

Thus,  is negative.

Substitue  in the above expression.

.

Answer 3

(3)

Find .

Double angle formula: .

From (1):   and .

Substitue   and in the above expression.

.

Answer 4

(4)

Find .

where .

Double angle formula: .

Substitute  in the above expression.

.