Question

Please help!
Find Tan x/2, given that tan x=-3 and x terminates in 90 degrees < x <180 degrees.

Answer 1

@calmat01 - can you help with this one?

Answer 2

This is a half angle problem. We need to use a half angle formula for it.

Answer 3

ok. the square root one?

Answer 4

That would be one we could use. But perhaps we could use eithr of the ones without the square root.

Answer 5

the one with the sin x in the numerator or denominator?

Answer 6

Let's use the one with the sine in the denominator.

Answer 7

ok

Answer 8

ok, first let us draw a triangle that fits the description of your problem.

Answer 9

Awesome! I wish I had 25 of you in my classroom!

Answer 10

you just made my daughter feel great! she took the reigns and drew it. She is feeling much better about this trig now than a couple of hours ago. You are fabulous!!!!

Answer 11

I have been doing this for 20 years. I know a good student when I see one. All it takes is a little guidance, and practice. She's the type of student I wish I had in all of my classes.

Answer 12

Ok, so, now we have our triangle, just fill in your values for cosine and sine of x.

Answer 13

\[(1-(- \sqrt{10}) /10)/((3\sqrt{10})/10)\]

Answer 14

Good job. Now simplify it. BTW, you wouldn't have had to rationalize the denominator in this case because they will just cancel out in the end.

Answer 15

i dont know how to simplify this

Answer 16

Think of it as a fraction divided by another fraction. Our rule is to multiply by the reciprocal.

So, it becomes\[\frac{ 1+\sqrt{10} }{ 10 } \times \frac{ 10 }{ 3\sqrt{10} }\]