prelim trig question (2 Viewers)

[elliottjohnson]

hey, the answer to sinx + cosx = 1 with 0<=x<=360


is 0, 90 , and another answer is 360 how does this 3rd answer come about?
thanks. using the a sin x + b cos x = r sin (x+alpha)

 

[khorne]

Third answer? what do you mean, 360?

Well 360 is the same as 0 on a unit circle, thus they have the same related angle and are the same.

 

[shady145]

yea and the question says between 0 and 360.

 

[khorne]

No it doesn't...it says less than or equal to

 

[elliottjohnson]

Third answer? what do you mean, 360?

Well 360 is the same as 0 on a unit circle, thus they have the same related angle and are the same.

well the fitz textbook has three sol'ns in the answers, so is 0 the same as 360?

 

[khorne]

Yeah, because on the unit circle, they are both 0Deg from the x-axis (considering there is one), so they have the same related angle. Also on the graphs, cos is 1 at 0,360 sin is 0 at those...

However, they are counted as separate solutions in this case I think (like a quadratic)

 

[elliottjohnson]

Yeah, because on the unit circle, they are both 0Deg from the x-axis (considering there is one), so they have the same related angle. Also on the graphs, cos is 1 at 0,360 sin is 0 at those...

However, they are counted as separate solutions in this case I think (like a quadratic)

ok, but this one has only one solution which is 33degrees41mins

3 cos x + 2 sin x = square root of 13 between 0<=x<=360

why wasnt the 360 - 33'41' counted?

 

[shady145]

No it doesn't...it says less than or equal to

yea thats wat i meant, too lazy to write the extra words. i said it coz as u say on the unit cricle, actually any circle u can keep rotating it till say 720 degrees where there would also lie an answer but we have a designated zone the answer is in. so it cant be 720

 

[shady145]

ok, but this one has only one solution which is 33degrees41mins

3 cos x + 2 sin x = square root of 13 between 0<=x<=360

why wasnt the 360 - 33'41' counted?

doesnt your formula say + not -, therefore, it will be larger than 360 which is out of the designated area and so is excluded

 

[elliottjohnson]

doesnt your formula say + not -, therefore, it will be larger than 360 which is out of the designated area and so is excluded

yer i thinkyour right i just need practise. thanks i think i get it now. ive just got to the signs right .

 

[Aquawhite]

Trig = most annoying maths topic invented.

 

[shady145]

Trig = most annoying maths topic invented.

no, probability is the only one that i cant be sure my answer is correct so its my most annoying math topic.