If Sin X = -4/5 and X is in Quadrant 4, then find Cos 2X
I have used the Double Angle ID and I got -7/25 as my answer.
However, here is where my problem is at. The question says that X is in Q4, so therefore Cos has to be positive right?
This was a question that I did on my Trig test and I got it wrong...the choices were...
A. -24/25
B. -7/25
C. 24/25
D. 7/25
I chose D because Cos is positive in Q4, however the correct answer was B, the exact same answer I got when I used the double angle formula...but it says X is in Q4????
Can somebody explain this to me please? Thanks!
omg someone please answer me
Cos (angle) is positive if the angle in is Q4
You only know that x is in Q4 ie 270 - 360 degrees so cos x is positive
But 2x would range between 540 (180) and 720 (360) degrees putting 2x in either Q3 or Q4 depending on what the original x actually was
And Cos (angle) is negative if the angle is in Q3
It could have been postive without doing the working out but when we applied the cos 2x formula we got a negative answer fixing 2x in Q3
cos 2x = 1 - 2sin^2 x
= 1 - 2(-4/5)^2
= 1 - 32/25
= -7/25
However if the question had said sin x = -1/5 and x is in Q4 we would have got:
cos 2x = 1 - 2sin^2 x
= 1 - 2(-1/5)^2
= 1 - 2/25
= 23/25
and so in this specific case 2x would have been in Q4