Precal Question

Question

if sec t 5 and the terminal point of t is in quadrant iii, use the identity sin^2(t/2)= 1-cos(t)/2 to find the exact value of (sin(t/2)+cos(t))

Answer 1

sect=5

sect=1/cost

1/cost=5

cost=1/5

sin(t/2)+cost=√((1-cost)/2)+cost=

√((1-0.2)/2)+0.2=

√(0.8/2)+0.2=

√(0.4)+0.2=

√(4/10)+0.2=

√(4/10)+(1/5)=

2/√10+(1/5)=

2√10/10 + (1/5)=

2√10/10 + (2/10)=

(2√10+2)/10=

(√10+1)/5