The Student Room Group

C3 Trigonometry



Since Cosθ = -1/3
then θ = 109°

So that means that θ is in the 1st and 4th quadrants right (as its positive in those)? So the solutions are 109°, and 360-109° = 250°

I've used this technique throughout C2 and C3 until I got stuck on this question and a few others where my method doesn't work???

So WHY is θ in quadrant 2 and 3 in this case? Its not like this in any other C3 question until now??
Reply 1
theta is positive in all quadrants

cos is positive in 1 and 4 and negative in 2 and 3

I am not sure what your problem is as your answers are correct

I do not understand why you suggest theta is in 1st quadrant when you know it is 109
Reply 2
Original post by TenOfThem
theta is positive in all quadrants

cos is positive in 1 and 4 and negative in 2 and 3

I am not sure what your problem is as your answers are correct

I do not understand why you suggest theta is in 1st quadrant when you know it is 109


Cos is positive in 1 and 4; so the answers should be 109°, and 360-109° = 251°
however, the answers are 109° and -109°..

I don't understand how..
Reply 3
251 is the same as -109 they are both is quadrant 3

depends what your range was
Reply 4
it says that cos theta is negative (-1/3)
therefore it will be in quadrants 2 and 3 (where cos is negative) as cos is positive in 1 and 4.
Reply 5
Original post by kirstiejs
it says that cos theta is negative (-1/3)
therefore it will be in quadrants 2 and 3 (where cos is negative) as cos is positive in 1 and 4.


I always used to use the THETA value, so if THETA is positive (which it is) then it is in the quadrants where THETA is positive... (in this case 1 and 4)?
Reply 6
theta is positive (or negative) in all 4 quadrants depending on wether you go clockwise or anticlockwise
Reply 7
Original post by TenOfThem
251 is the same as -109 they are both is quadrant 3

depends what your range was


The range was -180 to 180...
Reply 8
That is why you needed -109 instead of 251 then as 251 is outside of the range
Reply 9
Original post by TenOfThem
That is why you needed -109 instead of 251 then as 251 is outside of the range


Ohh !! I get it ! thanks a lot mate :smile:

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