If sin ø = .6 and cos ø >0, find sin 2ø and cos ø/2?

1 Answer
Jul 1, 2016

Answer:

sin 2t = 0.96
#cos (t/2) = 0.95#

Explanation:

sin t = 0.6. Find cos t.
#cos^2 t = 1 - sin^2 t = 1 - 0.36 = 0.64# --> #cos t = +- 0.8#
since cos t > 0 --> cos t = 0.8
sin 2t = 2sint.cos t = 2(0.6)(0.8) = 0.96
To find #cos (t/2)#, use the trig identity;
#2cos^2 a = 1 + cos 2a#
#2cos^2 (t/2) = 1 + cos t = 1 + 0.8 = 1.8#
#cos^2 (t/2) = 0.9#
#cos (t/2) = +- 0.95#
since cos t > 0, then, #cos (t/2) > 0#
#cos (t/2) = 0.95#