Given that cos 2a 14 and 0

Given that cos 2a = 1/4 and 0<2a<90, determine exact values of:

sin a

cos a

tan a

csc a

sec a

cot a

Solution

cos 2a = 1/4 and 0<2a<90

0<a<45

sin a=[1-cos2a] /2=[1-(1/4)] /2 =(3)/4

cos a=[1+cos2a] /2=[1+(1/4)] /2 =(5)/4  

tan a=sina/cosa=3/5

csc a=1/sina =4/3

sec a=1/cosa=4/5

cot a=1/tana=5/3