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# Help with trig c3 question watch

1. Hey,
I wondered if someone could explain to me how to answer this question (I've attached a pic of it).
When sin theta = -0.5, theta = 210 degrees and 330 degrees.

I got this answer, but I also got two more answers. My working basically goes wrong from here:
1/cos theta (1 + sin theta) = 0

Cos theta = 0 or sin theta = -0.5

So my question is, why isn't cos theta = 0 valid? Do you just ignore it?
Sorry this is long winded, I'm sure I could've written it much more simply lol
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2. (Original post by Phoebus Apollo)
Hey,
I wondered if someone could explain to me how to answer this question (I've attached a pic of it).
When sin theta = -0.5, theta = 210 degrees and 330 degrees.

I got this answer, but I also got two more answers. My working basically goes wrong from here:
1/cos theta (1 + sin theta) = 0

Cos theta = 0 or sin theta = -0.5

So my question is, why isn't cos theta = 0 valid? Do you just ignore it?
Sorry this is long winded, I'm sure I could've written it much more simply lol
If costheta = 0 then 1/costheta = what?
3. (Original post by Phoebus Apollo)
Hey,
I wondered if someone could explain to me how to answer this question (I've attached a pic of it).
When sin theta = -0.5, theta = 210 degrees and 330 degrees.

I got this answer, but I also got two more answers. My working basically goes wrong from here:
1/cos theta (1 + sin theta) = 0

Cos theta = 0 or sin theta = -0.5

So my question is, why isn't cos theta = 0 valid? Do you just ignore it?
Sorry this is long winded, I'm sure I could've written it much more simply lol
We have

If then we'd have a which is never a good thing. Ever try dividing by zero? It ruins your life.

If, on the other hand, we had: THEN would be valid.
4. (Original post by Phoebus Apollo)
Hey,
I wondered if someone could explain to me how to answer this question (I've attached a pic of it).
When sin theta = -0.5, theta = 210 degrees and 330 degrees.

I got this answer, but I also got two more answers. My working basically goes wrong from here:
1/cos theta (1 + sin theta) = 0

Cos theta = 0 or sin theta = -0.5

So my question is, why isn't cos theta = 0 valid? Do you just ignore it?
Sorry this is long winded, I'm sure I could've written it much more simply lol
Basically, I'm going to use x instead of theta as its more clear that way;

when you change sec x and tan x you should get
1/cosx + 2sinx/cosx = 0

then move one to the other side
2sinx/cosx = -1/cosx

Now you can multiply both sides by cos x to be left with;

2sinx = -1 ---> hence sin x = -1/2

Because cos x is the denominator, it cannot be zero because it gives an infinite number (thats why you get math error in your calculator)

So the only solution is sin x = -0.5
5. (Original post by Zacken)
We have

If then we'd have a which is never a good thing. Ever try dividing by zero? It ruins your life.

If, on the other hand, we had: THEN would be valid.
(Original post by kensaylo1)
Basically, I'm going to use x instead of theta as its more clear that way;

when you change sec x and tan x you should get
1/cosx + 2sinx/cosx = 0

then move one to the other side
2sinx/cosx = -1/cosx

Now you can multiply both sides by cos x to be left with;

2sinx = -1 ---> hence sin x = -1/2

Because cos x is the denominator, it cannot be zero because it gives an infinite number (thats why you get math error in your calculator)

So the only solution is sin x = -0.5
Thanks both!

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Updated: March 22, 2016
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