Question

If tan x = -4/3 and x is in quadrant 2, then cos2x = _____? (Will give medal and fan!)

A. -7/25
B. 7/25
C. -3/5
D. 3/5

Answer 1

@phi or @whpalmer4 ?

Answer 2

I have the answer, I just don't have a satisfactory explanation of how to get it!

Answer 3

Well, just do your best. If worse comes to worse then you can just give me the answer lol I won't complain

Answer 4

Is you are in quadrant 2, which trig functions are positive?

Answer 5

Likewise, every other trig function is negative in quad 2

Answer 6

I'm not quite sure...

Answer 7

Draw a triangle, using the fact that tan(x) = -4/3. That will give you two sides.
Solve for the other side, using the fact that ___ and ___ are positive in quad 2 to make sure all the sides have the right sign

Answer 8

These are what are positive in each quad

In quad one, all trig functions are postive.
Quad 3: Only tan(x) and cotan(x) are positive, cos(x) in quad 3 is negative

Answer 9

So then the answer would be either -7/25 or -3/5?

Answer 10

So draw a right triangle, using the fact that tan(x) = -4/3

Solve for the other side, making sure it has the right sign

Answer 11

cos(2x) is not in the same quad as x, just like cos(0.5) is not in quad 2 either

Answer 12

ohh... I'm so confused..

Answer 13

Do you see how I got the 2 sides?

Because x is doubled, the quadrant for 2x will be in quad 3 (I believe) @whpalmer4
Anyways, solve for the other side, then lets see if it should be positive or negitive