Find the exact value of the trigonometric ratio given that: sun u= -12/13, 3pi/2 <u< 2pi

Question

a) sin (u/2)

 

 

b) cos (2u)

 

c) tan (2u)

Answer 1

from the givens, u is in quadrant IV and the reference triangle has the well known 5-12-13 shape (one of the Pythag. triples that you should have in your memory). 

 

so now you know the cos u (it's positive 5/13, right?) and the half angle formula and the douible angle formulas can be used to compute the answers wanted in a, b, c.