Use a half-measure identity to find the indicated function value.

Question

tan t = −5/12 and sin t > 0; find tan 1/2t and sec 1/2t

Answer 1

tant = -5/12

sint= 5/13

cost = -12/13

sint>0

that means quadrant II, pi<t<pi/2

and pi/2<t/2<pi/

90<t/2<45

tant/2 = sint/2/cost/2

sint/2 = sqr(1-cost)/2) = sqr(1+12/13)/2) = sqr25/26 = 5/sqr26

cost/2 = sqr(1+cost)/2) = sq(1-12/13)/2) = sqr1/26= 1/sqr26

tant/2 = (5/sqr26)/(1/sqr26) = 5

tant/2 = sqr((1-cost)/(1+cost) = sqr(25/13)/1/13) =sqr25 = 5

tant = -5/12

t= 180-22.62= 157.38

t/2 = 157.38/2 = 78.7 degrees

tant/2 = tan78.7 = 5

sect/2 = 1/cost/2 = 1/1/sqr26 = sqr26