Question #b3353

2 Answers
Feb 29, 2016

tan 2u = 240/161.

Explanation:

Think of a right triangle with sides 8, 15, 17 --

82+152=172.

The angle at the hypoteneuse and the longer leg has a cosine of 15/17 and a sine of 8/17. Call that angle w.

Adding π to w gives angle u between π and 3π2, with cos u = -cos w = -15/17. Then sin u = -sin w = -8/17. Dividing the sine by the cosine gives tan u = 8/15.

Now use the double angle formula,

tan 2u
= 2tan u/(1-tan2u)

We have tan u = 8/15. So tan 2u = (16/15)/(1-64/225) = 240/161.

Feb 29, 2016

tan2u=240161

Explanation:

cosu=1517
sin2u=1225289=±6417
Since π<u<3π2 , then sinu=817
tanu=sinucosu=(817)(1715)=815
To find tan 2u apply the trig identity:
tan2u=2tanu1tan2u
Proceed numerically:
2tanu=2(815)=1615
(1tan2u)=164225=161225
Answer: tan2u=(1615)(225161)=240161