Find (a) sin 2t, (b) cos 2t, (c) tan 2t, and (d) the quadrant containing 2t.

Question

sin t = −7/25, cos t > 0

Answer 1

sint = - 7/25, cost > 0 → 270° < t < 360°

cost = 24/25

(a) sin2t = 2sintcost = 2(- 7/25)(24/25) = - 336/625;

(b)cos2t = 1 - 2sin²t = 1 - 2(49/625) = 527/625

(c) tan2t = sin2t/cos2t = - 336/527

(d) sin2t < 0, cos2t > 0, so, 2t in quadrant IV