How do you find csc ø/2 if sin ø = 8/17 using the equation π/2 <ø < π ?

1 Answer
Nghi N
Apr 6, 2018

#sin (t/2) = (4sqrt17)/17#

Explanation:

#sin t = 8/17#
#cos ^2 t = 1 - sin^2 t = 1 - 64/289 = 225/289#
#cos t = - 15/17# (t is in Quadrant 2)
To find #sin (t/2)#, use the trig identity:
#2sin^2 (t/2) = 1 - cos t = 1 + 15/17 = 32/17#
#sin^2 t = 32/34#
#sin (t/2) = (4sqrt2)/sqrt34 = (4sqrt68)/34 = (4sqrt17)/17#

Related questions
Impact of this question
587 views around the world
You can reuse this answer
Creative Commons License