Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have sin a + cos a = 1/3

Use the fact that sin 2a = 2*(sin a)(cos a)

sin a + cos a = 1/3

square the right and left hand sides

(sin a + cos a)^2 = (1/3)^2

=> (sin a)^2 + (cos a)^2 + 2*(sin a)(cos a) = 1/9

(sin a)^2 + (cos a)^2 = 1

=> 1 + 2*(sin a)(cos a) = 1/9

=> 2*(sin a)(cos a) = 1/9 - 1

=> 2*(sin a)(cos a) = -8/9

=> sin 2a = -8/9

The required value of sin 2a = -8/9

 

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial