If cos(x) = (1/4), where x lies in quadrant 4, how do you find cos(x + pi/3)?

1 Answer
Mar 12, 2017

Answer:

#\cos(x+(\pi/3))={1+3\sqrt{5}}/8#, approximately #0.964#.

Explanation:

First off, since #x# is in quadrant #4# below the horizontal axis, its sine is negative:

#\sin(x)=-\sqrt{1-(1/4)^2}=-\{sqrt{15}}/4}#

Then, apply the formula for the cosine of a sum:

#\cos(color(blue)(x)+color(gold)(\pi/3))=color(blue)(\cos(x))color(gold)(\cos(\pi/3))-color(blue)(\sin(x))color(gold)(\(sin\pi/3))#

#=(1/4)(1/2)-({-\sqrt{15}}/4)(\{\sqrt{3}}/2)#

#={1+3\sqrt{5}}/8#