The use of identical sign in C3

Original post by coconut64

Hi, I would like to know when the identical sign is used in C3 because it is used when proving trigonometric identities but why isn't it used when solving algebraic addition/ multiplication questions?

Thanks

Can you give an example please?
The identical sign is used when both sides are exactly the same for all values of x. In trigonometric identities, the identities used itself have the identical sign e.g.

sin^2x + cos^2x \equiv 1

because it works for all values of x. Therefore, trigonometric identities are proved using those identities which are all identical lol (if u get me).

(edited 7 years ago)

Reply 2

NotNotBatman

20

Original post by coconut64

Hi, I would like to know when the identical sign is used in C3 because it is used when proving trigonometric identities but why isn't it used when solving algebraic addition/ multiplication questions?

Thanks

Use equivalent sign When LHS is equivalent to RHS for all values of the variable.

Reply 3

OP

Original post by Chittesh14

Can you give an example please?
The identical sign is used when both sides are exactly the same for all values of x. In trigonometric identities, the identities used itself have the identical sign e.g.

sin^2x + cos^2x \equiv 1

Yes, I understand that but sometimes when you are proving the identities, you have to multiply the fraction by a factor though. For example in this question: x+2/（x+2）（x+3） - x+5/(x+2)(x+7) , if you are asked to simplify this into a single fraction why do you only use this = sign instead of ≡ ?

Thanks

Reply 4

NotNotBatman

20

Original post by coconut64

Yes, I understand that but sometimes when you are proving the identities, you have to multiply the fraction by a factor though. For example in this question: x+2/（x+2）（x+3） - x+5/(x+2)(x+7) , if you are asked to simplify this into a single fraction why do you only use this = sign instead of ≡ ?

Thanks

You can't divide by 0, you can substitute a value of x in the rhs but on the lhs it will be undefined, so it isn't equal for all values of x.

Reply 5

OP

Original post by NotNotBatman

You can't divide by 0, you can substitute a value of x in the rhs but on the lhs it will be undefined, so it isn't equal for all values of x.

so a ≡ sign can only be used when both sides of the equations equal to each other for all values of X?

Thanks

Reply 6

Original post by coconut64

so a ≡ sign can only be used when both sides of the equations equal to each other for all values of X?

Thanks

Yeah, as I said earlier. It is only equivalent for all values of x.
For example, 90x + 90 = 50 + 10x is the same as 80x = -40 and once you solve it, x = -1/2. This value of x satisfies the equation only, if you substitute x = 3 or 4 or 5 or -2, none will work. The only way it is identical is if both the LHS and RHS are equal e.g.

90x + 90

\equiv

90x + 90
90x + 90

\equiv

90(x + 1) etc.

Reply 7

Original post by coconut64

so a ≡ sign can only be used when both sides of the equations equal to each other for all values of X?

Thanks

Are you on Chapter 1 of C3?

Reply 8

OP

Original post by Chittesh14

Are you on Chapter 1 of C3?

Erm... Not really, I have finished C3 already just didn't really get when to use the identical sign. It was something that was niggling me for a while cuz I didn't get it. Thanks

Reply 9

Original post by coconut64

Erm... Not really, I have finished C3 already just didn't really get when to use the identical sign. It was something that was niggling me for a while cuz I didn't get it. Thanks

Oh wow, that's amazing. You're quite fast :wink:

did you start early or normal but put in a lot of effort? Also, how did you find the module btw (overall)? and no problem.

Reply 10

OP

Original post by Chittesh14

Oh wow, that's amazing. You're quite fast :wink:

did you start early or normal but put in a lot of effort? Also, how did you find the module btw (overall)? and no problem.

Basically straight after I finished my AS exams, we moved straight into C3 so by the end of A1 before summer, we had covered half of c3 already. Then back to college for another 2 months to finish it off. People in my year actually got forced to do a mock on the 2016 paper recently, which is ridiculous cuz we barely got full grasp of the topic.. But yh

Reply 11