Question

Suppose that tan t = 5/12 and sin t < 0. Find cos(2t) by hand using identities.
a. 119/169
b. -(sqrt26)/26
c. 120/169
d. (5(sqrt26))/26

Answer 1

Draw a triangle... this will help a lot. \[\large \tan t = \frac{ 5 }{12 }\] and tan is opposite/adjacent so:

Find x using pythagoras, then you can find sin(t) and/or cos(t), and then you'll probably want to use double angle formulas for cos(2t) ( http://mathworld.wolfram.com/Double-AngleFormulas.html)

Answer 2

Note that since tan(t) is positive, sin(t) is negative (less than zero) then cos(t) must also be negative, so that means t must be in the third quadrant: http://www.sciencedigest.org/UnitCircle.gif

So... \[\large \pi \le t \le \frac{ 3 \pi }{ 2}\]

Answer 3

all I want to say is that is one of the smoother diagrams I have seen on here @agent0smith

Answer 4

@whatisthequestion thanks :)