If tanθ= 7/24 and θ is in quadrant iii

Question

Find:

a) cos2θ

b) cos θ/2

Answer 1

tanT=7/24

cosT= -24/25

sinT=-7/25

cos2T= cos^2(T) - sin^2(T)= (24^2-7^2)/25^2

= (576-49)/625= 527/645= about =.843

cos(T/2)= -sqr(1-cosT)/2= -1/5sq2

=-sqr2/10= about -.1414

check the answers

T=about 16.26+180=196.26 degrees

T/2= 98.13

cos98.13= -.1414

2T=2(196.26)= 392.52

cos392.52= cos32.52=.843