Even-Odd Identities

[PowerXtremeBaby]

My trig class is using a book that hasn't been published yet, we're the first class to use it and it is totally unhelpful.

Use even-odd identities to solve each equation. Find all solutions over the interval [0,2pi]. Verify your solutions by graphing.


1) Tan(-x)= -2.5
I got as far as:
-sinx/cosx=-2.5
and now i'm stuck.
I know the identity is tan(-x)=-tan(x), but I don't know how to use that to help me.

2) 2.4= (cos(-x)/2)+1
I don't even know where to start.
Identity is cos(-x)=cos(x)?

3) 2(sin(-x)/tanx)=0.8
So far I have 2(sin(-x)/(sin(x)/cos(x))=0.8
and then I flipped the bottom fraction and multiplied:
2(sin9-x)X(cos(x)/sin(x)=0.8
I know the sins can cancel, but I forget how to do it where one is negative and one is positive.

and I don't understand what it wants as the answer.
I'm completely lost! My professor doesn't seem to understand what he is trying to teach, so I don't understand it.

 

[Aladdin]

My trig class is using a book that hasn't been published yet, we're the first class to use it and it is totally unhelpful.

Use even-odd identities to solve each equation. Find all solutions over the interval [0,2pi]. Verify your solutions by graphing.


1) Tan(-x)= -2.5
I got as far as:
-sinx/cosx=-2.5
and now i'm stuck.
I know the identity is tan(-x)=-tan(x), but I don't know how to use that to help me.

2) 2.4= (cos(-x)/2)+1
I don't even know where to start.
Identity is cos(-x)=cos(x)?

3) 2(sin(-x)/tanx)=0.8
So far I have 2(sin(-x)/(sin(x)/cos(x))=0.8
and then I flipped the bottom fraction and multiplied:
2(sin9-x)X(cos(x)/sin(x)=0.8
I know the sins can cancel, but I forget how to do it where one is negative and one is positive.

and I don't understand what it wants as the answer.
I'm completely lost! My professor doesn't seem to understand what he is trying to teach, so I don't understand it.

. . . . . .\(\displaystyle For \ the \ first \ one \ \tan(-x)=-2.5\)

. . . . . .\(\displaystyle -tan(x)=-2.5\) - Multiply both sides by ( - ) ,

. . . . . .\(\displaystyle tan(x)=2.5\)

\(\displaystyle I\ would\ have\ to\ use\ a\ calculator\ as\ the\ answer\ has\ no\ analytic\ form\ using\ the \arctan(2.5)\ button.\)

. . . . . .\(\displaystyle 2*) \ 2.4=\frac{cos(-x)}{2}+1\)

. . . . . .\(\displaystyle 2.4=\frac{cos(x)+2}{2}\)

. . . . . .\(\displaystyle 2(2.4)=cos(x)+2\)

. . . . . .\(\displaystyle 4.8 - 2 =cos(x)\)

. . . . . .\(\displaystyle 2.8=cos(x)\) 0=<cos(x)<=1 ---- How come ?

. . . . . .\(\displaystyle Use \ the \ calculator .\)

 

[Deleted member 4993]

My trig class is using a book that hasn't been published yet, we're the first class to use it and it is totally unhelpful.

Use even-odd identities to solve each equation. Find all solutions over the interval [0,2pi]. Verify your solutions by graphing.

1) Tan(-x)= -2.5 <<< This is not a standard angle. Are you allowed to use calculator?
I got as far as:
-sinx/cosx=-2.5
and now i'm stuck.
I know the identity is tan(-x)=-tan(x), but I don't know how to use that to help me.

2) 2.4= (cos(-x)/2)+1
I don't even know where to start.
Identity is cos(-x)=cos(x)?

2.4 = cos(x)/2 + 1

cos(x) = 2.8 <<< |cos(x)| ? 1 - so there is no solution for the given identity


3) 2(sin(-x)/tanx)=0.8
So far I have 2(sin(-x)/(sin(x)/cos(x))=0.8
and then I flipped the bottom fraction and multiplied:
2(sin9-x)X(cos(x)/sin(x)=0.8
I know the sins can cancel, but I forget how to do it where one is negative and one is positive.

and I don't understand what it wants as the answer.
I'm completely lost! My professor doesn't seem to understand what he is trying to teach, so I don't understand it.

 

[PowerXtremeBaby]

Thank you, and I ended up figuring out the last one as 1.98 I think.
I put number 2 as undefined before i read this.