Suppose that tan(a)= 3/4 and π ,a.3π/2, find sin(2a) and cos(2a)

Question

Suppose that tan(a)= 3/4 and π ,a.3π/2, find sin(2a) and cos(2a)

Answer 1

You will need to find sine and cosine first.  The use the double-angle identity to evaluate.

 

Use the tangent-secent identity to find sine and cosine.

 

1 + tan²a = sec²a

 

1 + tan²a = 1 / cos²a

 

1 + (3/4)² = 1 / cos²a

 

1 + (9/16) = 1 / cos²a

 

(16 + 9) / 16 = 1 / cos²a

 

25 / 16 = 1 / cos²a

 

 

Square-root both sides of the equation.

 

5 / 4 = 1 / cos(a)

 

5cos(a) = 4

 

  cos(a) = 4/5

 

 

sin(a) = tan(a)cos(a)

sin(a) = (3/4)(4/5)

sin(a) = 3/5

 

 

Now you can use the values of sin(a) and cos(a) to find sin(2a) and cos(2a).

 

sin(2a) = 2sin(a)cos(a)

 

cos(2a) = 1 - 2sin²(a)

 

 

Plug in the values to evaluate.