# trigonometry

• Oct 30th 2008, 07:32 AM
patranka
trigonometry
cosa-sina=0
or
cosa+sina=1

how to find a?
the only why which i came out with is to square, but i think if i do so i'll lose (not always but sometimes) several meanings of a..
i hope you understood what i was trying to say (Nod)
• Oct 30th 2008, 07:56 AM
ajj86
Solution
cosa-sina=0
or
cosa+sina=1

I was thinking you could square the bottom equation to get:
(cosa)^2 + 2cosasina + (sina)^2 = 1

Group terms to get:
(cosa)^2 + (sina)^2 + 2cosasina = 1

The first two terms form the identity:
(cosa)^2 + (sina)^2 = 1

So, using substitution:
1 + 2cosasina = 1
which reduces to:
2cosasina = 0

Now, the above forms the double angle identity:
sin2a = 2sinacosa

So, using substitution:
sin2a = 0

Now, we have to figure what angles would cause sin2a = 0:
0, +/- Pi/2, +/- Pi, +/- 3Pi/2,...

Normally, these angles would cause sin to equal 1 or -1, but since it is 2 times the angle it causes sin2a to equal zero.

a is written of the form:

a = +/- (n*Pi/2) for some n = 0, +/-1, +/-2,...

Part 2.

Do the same for the first equation:
(cosa)^2 - 2cosasina + (sina)^2 = 0

Again, use the identity:
(cosa)^2 + (sina)^2 = 1

Substitute:
1-2cosasina = 0