Trigonometry - finding the appropriate angle

[david18]

Homework Statement

"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?

 

[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

 

[HallsofIvy]

Homework Statement

"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?

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

 

[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 I am pretty sure its right

 

[rock.freak667]

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 I am pretty sure its right

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

which can be easily obtained by dividing by cosA

 

[Tedjn]

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

 

[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.