Question

Select all the solutions from the list below for cos3A - sin3A = 1 for 0º≤A≤360º.
a)90 degree
b)0 degree
c)360 degree
d)270 degree

Answer 1

It'd be nice if you don't make a habit of this, but if you're in any sort of hurry, you could exploit the fact that it's multiple choice and just test out the choices if they work, go ahead and do that while I think of the least stressful way to go about this if there weren't any choices.

Answer 2

Ok, I think I've found a way to do it, are you still up for it?

Answer 3

yes

Answer 4

actuall never mind lol i already answer that question yesterday opps but could u help me with another

Answer 5

Well, regardless XD
Remember these:
cos 3A - sin 3A = 1 (1)
cos 3A = 1 + sin 3A (2)
cos 3A - 1 = sin 3A (3)

and this IDENTITY
sin² x = 1 - cos² x

Now we begin.
cos 3A - sin 3A = 1 (Starting equation)(1)
cos 3A = 1 + sin 3A (Addition Property of Equality)[leads to Equation (2)]
cos² 3A = 1 + 2sin 3A + sin² 3A (squaring both sides)
cos² 3A = 1 + 2(cos 3A - 1) + sin² 3A [Because of Equation (3)]
cos² 3A = 1 + 2(cos 3A - 1) + 1 - cos² 3A (The [Pythagorean] identity)
cos² 3A = 2cos 3A - cos² 3A (Simplifying)
2cos² 3A - 2cos 3A = 0 (Addition Property of Equality)
cos² 3A - cos 3A = 0 (Dividing both sides of the equation by 2)
(cos 3A)[(cos 3A) - 1] = 0 (Factoring out cos 3A)
And the rest is easy

And lol, sure hit me :D

Answer 6

but just to make sure its 90 degrees right :

Answer 7

The question implied that there may be more than one solution, and you better believe it ;)

Answer 8

ohh yeah well is 90 a possible answer lol

Answer 9

That's right. If you're absolutely sure you've got this question down, go ahead and give the other one :)

Answer 10

lol and 270 too right ?? and okay

Answer 11

Just saying;
0 degrees is pretty much the same as 360 degrees, and
cos 0 = 1
sin 0 = 0

Again, just sayin' ;)

Answer 12

huh?? lol im talking about 270 though:)

Answer 13

as being another possible right answer:)

Answer 14

You might want to reconsider that, though.

Answer 15

Never mind :D My bad

Answer 16

???? oh okay so i guess that ones wrong lol

Answer 17

You mentioned another question?

Answer 18

oh haha okay :)

Answer 19

yeah im write it down now

Answer 20

The solutions for sinA + sin2A = 0 for 0º≤A≤360º are

i think this might be the answer but im not sure
0º; 120º; 180º; 240º; 360º

Answer 21

ps can u give me a video that has more info about teaching this stuff /
if u want ?:)

Answer 22

I don't have any. :(
Now working on your question, hang on...

Answer 23

oh okay:)

Answer 24

Okay, you'll appreciate the use of this later, probably.
First, it'll be convenient to see immediately that if sin A is 0, then, A could only be either 0 or 180, right?

Answer 25

yeah?

Answer 26

Well, then if sin 0 = 0, then sin 2(0) = 0, right?
also, if sin 180 = 0, then sin 2(180) = 0
so 0 and 180 are solutions, yes?

Answer 27

Since for A = 0 or A = 180
sin A + sin 2A = 0

Answer 28

yeah

Answer 29

Ok, it works for 360 too. Now, there's a reason I wanted to rule that out:
You know the identity for
sin 2A
?

Answer 30

umm no

Answer 31

sin 2A = 2sinAcosA
ok?

Answer 32

yes:)

Answer 33

Now
\[\sin A + \sin 2A = 0\]\[\sin A + 2\sin A \cos A=0\]\[\sin A = -2\sin A \cos A\]
Now, we have to assume sin A is not 0, otherwise the next step is dubious, which is dividing both sides by sin A

Answer 34

okay..
u get
1=-sinAcosA??

Answer 35

No... You get
1 = -2cos A
right?

Answer 36

oh ok

Answer 37

then divied by -2 right

Answer 38

That's right, so
cos A = -1/2
What do you get?

Answer 39

cosA= -1/2

Answer 40

yes, so
A = ?
Well, you could memorise these things, but if
cos A = -1/2
Then
A could be {120, 240}

Answer 41

Which means you were RIGHT the first time :D
You did well :D

Answer 42

ohh okay thanks lol:)

Answer 43

i have another one if u would like to help:)

Answer 44

I'm still here, and go ahead.

Answer 45

Solve 2cos2θ/2 = cos2θ for 0º≤θ≤360º. (Hint: Graph each side of the equation and find the points of intersection.)

okay thanks