A Few Basic Questions (1 Viewer)

[GaDaMIt]

1) What do you do with a question when there is absolute values on both sides?

eg
|2x - 1| = |x + 5|


2) What is the answer to
"Find theta correct to the nearest minute if tan theta = 1.7"

Answers say only 59'32'. I thought it was 59'32' and (180+59'32') 239'32'? Is there something I missed?


3) 4 tan theta + 1 - tan^2 theta = sec^2 theta

Answers say theta = 0, 63, 143, 180, 360

143 = typo right?

 

[Riviet]

1) Take 4 cases: both sides are positive, LHS is positive and RHS is negative, LHS is negative and RHS is positive, both sides are negative.
Edit: you will notice you will get two answers repeated, ie x=6 twice and x=-4/3 twice if you do it this way.
2) Check for any restriction on θ in the question. If there's none, then I guess the answers are wrong.

3) Yep, it should be 243 degrees, the 3rd quadrant angle.

 

[GaDaMIt]

1) Take 4 cases: both sides are positive, LHS is positive and RHS is negative, LHS is negative and RHS is positive, both sides are negative.

I don't get? Mind doing the example question so i can see?

2) Check for any restriction on θ in the question. If there's none, then I guess the answers are wrong.

No restriction on the question ..

 

[pLuvia]

1. Can either be: |2x - 1| = |x + 5|
(2x-1)=(x+5)
(2x-1)=-(x+5)
-(2x-1)=(x+5)
-(2x-1)=-(x+5)

2. The author is just lazy and couldn't be bothered with adding the other answer

 

[Riviet]

1) Ok, a better way to do it. We know that absolute value makes anything positive. Therefore we are allowed to square both sides since it doesn't affect the equation:
(2x-1)²=(x+5)²
4x²-4x+1=x²+10x+25
3x²-14x-24=0
(3x+4)(x-6)=0
x=-4/3, 6

 

[onebytwo]

1) Ok, a better way to do it. We know that absolute value makes anything positive. Therefore we are allowed to square both sides since it doesn't affect the equation:
(2x-1)²=(x+5)²
4x²-4x+1=x²+10x+25
3x²+14x-24=0
(3x+4)(x-6)=0
x=-4/3, 6

you mean 3x^2 - 14x -24 = 0

 

[Riviet]

Thanks for spotting that, fixed now. ;D