Question

Given: cos(theta) = -4/5 , sin x = -12/13, theta is in the third quadrant, and x is in the fourth quadrant; evaluate tan(1/2)(theta)

-3
3
1/3

Answer 1

@dpaInc

Answer 2

So I know that tan = 3/4 (from the last problem) but do I just multiply that by 1/2? Because that would make it 3/8 but that's not a choice... What do I do?

Answer 3

@saifoo.khan

Answer 4

is this the question: \(\large tan(\frac{\theta}{2})= \) ????

Answer 5

Yes

Answer 6

ok.. do you know the half-angle formula for tangent?

Answer 7

nvmd... i'll put it up..

Answer 8

\(\huge tan(\frac{\theta}{2})=\pm\sqrt{\frac{1-cos\theta}{1+cos\theta}} \)

Answer 9

now you already have the value for cos(theta). what was it???

Answer 10

Oh right right right!! I forgot the formulas part.. & cos(theta)=3/4

Answer 11

the problem says cos(theta) = -4/5

Answer 12

Whoops, that was tan.. Embarassing.

Answer 13

sawright... :)

Answer 14

So would that give you 9?

Answer 15

so....
\(\large tan(\frac{\theta}{2})=\pm\sqrt{\frac{1-(-4/5)}{1+(-4/5)}} \)
simplify this....
then we'll determine which one it is... (positive or negative)

Answer 16

the top would be 9/5 and the bottom 1/5 then you would get 9 & you have to sqrt it. So it would be +/- 3