Using the double angle formula, it's characteristics and applications
$begingroup$
So I know the double angle formula is
$$
2 sin alpha cos alpha = sin(2alpha)
$$
I have this equation :
$$
2sin(mx+ny)(cos(mx+ny))m
$$
Now according to the answers sheet if I use the double angle formula I get
$$
2msin(2mx + 2ny)
$$
But according to the formula, wouldn't I have to multiply only $alpha$ by $2$?
According to me, I would get
$$
sin(2mx+2ny)m, ~~text{without the 2 upfront.}
$$
Can somebody please explain what I'm doing wrong? Or what I'm not understanding correctly?
Does the formula
$$
2 sin cosalpha cos alpha = sin(2alpha) ~~~text{imply}~~ 2sin(2alpha) ~~~text{?}$$
A photo of the problem for reference:
trigonometry
asked Dec 14 '18 at 11:20
BM97BM97
758
$endgroup$
add a comment |
$begingroup$
So I know the double angle formula is
$$
2 sin alpha cos alpha = sin(2alpha)
$$
I have this equation :
$$
2sin(mx+ny)(cos(mx+ny))m
$$
Now according to the answers sheet if I use the double angle formula I get
$$
2msin(2mx + 2ny)
$$
But according to the formula, wouldn't I have to multiply only $alpha$ by $2$?
According to me, I would get
$$
sin(2mx+2ny)m, ~~text{without the 2 upfront.}
$$
Can somebody please explain what I'm doing wrong? Or what I'm not understanding correctly?
Does the formula
$$
2 sin cosalpha cos alpha = sin(2alpha) ~~~text{imply}~~ 2sin(2alpha) ~~~text{?}$$
A photo of the problem for reference:
trigonometry
asked Dec 14 '18 at 11:20
BM97BM97
758
$endgroup$
4
$begingroup$
The answer sheet is wrong. You are correct.
$endgroup$
– drhab
Dec 14 '18 at 11:23
1
$begingroup$
One more typo in a textbook !
$endgroup$
– Claude Leibovici
Dec 14 '18 at 11:27
$begingroup$
Thanks ! May you please check the picture that i uploaded and still tell me if im right? Maybe i'm missing something or i dont know
$endgroup$
– BM97
Dec 14 '18 at 11:49
add a comment |
$begingroup$
So I know the double angle formula is
$$
2 sin alpha cos alpha = sin(2alpha)
$$
I have this equation :
$$
2sin(mx+ny)(cos(mx+ny))m
$$
Now according to the answers sheet if I use the double angle formula I get
$$
2msin(2mx + 2ny)
$$
But according to the formula, wouldn't I have to multiply only $alpha$ by $2$?
According to me, I would get
$$
sin(2mx+2ny)m, ~~text{without the 2 upfront.}
$$
Can somebody please explain what I'm doing wrong? Or what I'm not understanding correctly?
Does the formula
$$
2 sin cosalpha cos alpha = sin(2alpha) ~~~text{imply}~~ 2sin(2alpha) ~~~text{?}$$
A photo of the problem for reference:
trigonometry
asked Dec 14 '18 at 11:20
BM97BM97
758
$endgroup$
So I know the double angle formula is
$$
2 sin alpha cos alpha = sin(2alpha)
$$
I have this equation :
$$
2sin(mx+ny)(cos(mx+ny))m
$$
Now according to the answers sheet if I use the double angle formula I get
$$
2msin(2mx + 2ny)
$$
But according to the formula, wouldn't I have to multiply only $alpha$ by $2$?
According to me, I would get
$$
sin(2mx+2ny)m, ~~text{without the 2 upfront.}
$$
Can somebody please explain what I'm doing wrong? Or what I'm not understanding correctly?
Does the formula
$$
2 sin cosalpha cos alpha = sin(2alpha) ~~~text{imply}~~ 2sin(2alpha) ~~~text{?}$$
A photo of the problem for reference:
trigonometry
trigonometry
asked Dec 14 '18 at 11:20
BM97BM97
758
asked Dec 14 '18 at 11:20
BM97BM97
758
edited Dec 14 '18 at 11:53
BM97
asked Dec 14 '18 at 11:20
BM97BM97
758
asked Dec 14 '18 at 11:20
BM97BM97
758
asked Dec 14 '18 at 11:20
BM97BM97
758
758
4
$begingroup$
The answer sheet is wrong. You are correct.
$endgroup$
– drhab
Dec 14 '18 at 11:23
1
$begingroup$
One more typo in a textbook !
$endgroup$
– Claude Leibovici
Dec 14 '18 at 11:27
$begingroup$
Thanks ! May you please check the picture that i uploaded and still tell me if im right? Maybe i'm missing something or i dont know
$endgroup$
– BM97
Dec 14 '18 at 11:49
add a comment |
4
$begingroup$
The answer sheet is wrong. You are correct.
$endgroup$
– drhab
Dec 14 '18 at 11:23
1
$begingroup$
One more typo in a textbook !
$endgroup$
– Claude Leibovici
Dec 14 '18 at 11:27
$begingroup$
Thanks ! May you please check the picture that i uploaded and still tell me if im right? Maybe i'm missing something or i dont know
$endgroup$
– BM97
Dec 14 '18 at 11:49
4
4
$begingroup$
The answer sheet is wrong. You are correct.
$endgroup$
– drhab
Dec 14 '18 at 11:23
$begingroup$
The answer sheet is wrong. You are correct.
$endgroup$
– drhab
Dec 14 '18 at 11:23
1
1
$begingroup$
One more typo in a textbook !
$endgroup$
– Claude Leibovici
Dec 14 '18 at 11:27
$begingroup$
One more typo in a textbook !
$endgroup$
– Claude Leibovici
Dec 14 '18 at 11:27
$begingroup$
Thanks ! May you please check the picture that i uploaded and still tell me if im right? Maybe i'm missing something or i dont know
$endgroup$
– BM97
Dec 14 '18 at 11:49
$begingroup$
Thanks ! May you please check the picture that i uploaded and still tell me if im right? Maybe i'm missing something or i dont know
$endgroup$
– BM97
Dec 14 '18 at 11:49
add a comment |
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4
$begingroup$
The answer sheet is wrong. You are correct.
$endgroup$
– drhab
Dec 14 '18 at 11:23
1
$begingroup$
One more typo in a textbook !
$endgroup$
– Claude Leibovici
Dec 14 '18 at 11:27
$begingroup$
Thanks ! May you please check the picture that i uploaded and still tell me if im right? Maybe i'm missing something or i dont know
$endgroup$
– BM97
Dec 14 '18 at 11:49