Find sin theta, given that cos 2 theta = 1/4 and 0< theta < pie /2 ?

1 Answer
Mar 26, 2018

Answer:

#sin t = sqrt6/4#

Explanation:

Use trig identity:
#2sin^2 t = 1 - cos 2t#
In this case, #cos 2t = 1/4# -->
#2sin^2 t = 1 - 1/4 = 3/4#
#sin^2 t = 3/8#
#sin t = +- sqrt3/(2sqrt2) = +- sqrt6/4#
In the interval #(0, pi/2)#, sin t is positive
#sin t = sqrt6/4#