Homework Help: Trigonometry - finding the appropriate angle

1. Jan 29, 2008

david18

1. The problem statement, all variables and given/known data

"Find the least positive value of the angle A for which:

cosA = sinA and both are negative."

Im having some trouble on this one as usually i would be given cosA=-0.2 or something but this has no figures... Any help?

2. Jan 29, 2008

david18

Oh i think i solved it now I divided both sides by cosA to get tan and then added 180 to 45 which gives me 225 - both sin 225 and cos 225 are negative whereas cos45 and sin45 arent

3. Jan 29, 2008

HallsofIvy

??? there is no such number! cos(A) is negative for 90o< A< < 270. sin(A) is negative for 180o< A< 360o. cos(A) and sin(A) are both negative for any A between 180o and 270o. But there is no smallest A in that interval!

4. Jan 29, 2008

david18

it says cosA=sinA meaning that sin225 is equal to whatever cos225 equals (i checked on calcualtor and they were the same.

The answer book also said 225 so Im pretty sure its right

5. Jan 29, 2008

rock.freak667

Then why is the answer not uhm...45?

which can be easily obtained by dividing by cosA

6. Jan 29, 2008

Tedjn

The answer can't be 45, because of the precondition that sine and cosine must be negative.

7. Jan 30, 2008

HallsofIvy

How silly of me! I completely overlooked the "sin x= cos x".

Yes, as I said before, sine and cosine are first both negative between 180 and 270 degrees. The smallest value for which sine and cosine are both negative and sin(x)= cos(x) is 180+ 45= 225 degrees.