csc a=2, pi/2<a<pi find sin a, cos a, tan a

Expert Answers

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

given: cosec a = 2 and  `pi/2 < a < pi`

cosec is inverse of sine, thus

csc a = 1/sin a = 2

or, sin a = 1/2

cos a = `sqrt (1-sin^2 a) = sqrt(1-(1/2)^2) = sqrt (1-1/4) = sqrt (3/4) = - sqrt 3/2`

and tan a = `sina /cosa = (1/2)/(-sqrt3/2) = -1/sqrt3`  

we chose negative signs for cos and tan, since a is between pi/2 and pi, and between these ranges, cos a and tan a will be negative.

Hope this helps.

Approved by eNotes Editorial Team

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