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# c4 compound angles watch

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1. Express where R > 0 and is an acute angle.

I have no idea what to do.... I got 3 = Rcosx and 7 = Rsinx, but I'm not sure If i'm doing the right direction to get the answer and
2. tan (alpha) = (7/3) -------------(from Rsin(alpha)/Rcos(alpha)=7/3)
Then sub in to get R to one of the previous two equations
3. (Original post by KingPin)
tan (alpha) = (7/3) -------------(from Rsin(alpha)/Rcos(alpha)=7/3)
Then sub in to get R to one of the previous two equations
correct, pretty simple rlly.
4. (Original post by piccolo12345)
Express where R > 0 and is an acute angle.

I have no idea what to do.... I got 3 = Rcosx and 7 = Rsinx, but I'm not sure If i'm doing the right direction to get the answer and
That's right. Time to get the calc out to get alpha.

EDIT: I meant the textbook was right.
5. use R^2(sin^2a+cos^2a) to find R
6. (Original post by KingPin)
tan (alpha) = (7/3) -------------(from Rsin(alpha)/Rcos(alpha)=7/3)
Then sub in to get R to one of the previous two equations
How do the answers get alpha as 23.2? I'm supposed to do this by putting tan^-1(7/3) in the calculator arent I? which gets 66.8
7. (Original post by piccolo12345)
How do the answers get alpha as 23.2? I'm supposed to do this by putting tan^-1(7/3) in the calculator arent I? which gets 66.8
tanx = 3/7 in this case, he did it wrong. And it was a pointless post, because you already had R = sqrt58 and an expression for alpha.
8. (Original post by Physics Enemy)
tanx = 3/7 in this case, he did it wrong. And it was a pointless post, because you already had R = sqrt58 and an expression for alpha.
Sorry, I went from his results...lazy I know
9. (Original post by Physics Enemy)
tanx = 3/7 in this case, he did it wrong. And it was a pointless post, because you already had R = sqrt58 and an expression for alpha.
Oh did I get the 3 and 7 mixed up at the start?
And so now I've got alpha as 23.2

So now to find R, I substitute it into an equation, so R = 3/cos(23.2), which gets 3.26??
10. (Original post by piccolo12345)
Oh did I get the 3 and 7 mixed up at the start?
And so now I've got alpha as 23.2

So now to find R, I substitute it into an equation, so R = 3/cos(23.2), which gets 3.26??
Rsin(x + a) = (Rcosa)sinx + (Rsina)cosx
Rcosa = 7, Rsina = 3
R^2 = 58 => R = Sqrt(58)
a = sin^-1[3/Sqrt(58)]

Yes you got them mixed up. And no I wouldn't use the angle to get R.
11. I always find it easy to remember the proof (then again, I know a lot of people who can't). But remember your double angle formula:

So looking at the question:

So
Therefore:
12. (Original post by Physics Enemy)
Rsin(x + a) = (Rcosa)sinx + (Rsina)cosx
Rcosa = 7, Rsina = 3
R^2 = 58 => R = Sqrt(58)
a = sin^-1[3/Sqrt(58)]

Yes you got them mixed up. And no I wouldn't use the angle to get R.
Cheers
13. (Original post by Wednesday Bass)
I always find it easy to remember the proof (then again, I know a lot of people who can't). But remember your double angle formula:

So looking at the question:

So
Therefore:
You mind helping me on part c, although i dont think they are related. i got so much to learn for the exam in a few weeks @@@@@@@@@

Question is

ci) Given that is an acute angle and tan , show that

ii) Hence show that where p is a rational number

ii uses the double angle formula im guessing but i dont know what to do at all for part i)
14. (Original post by piccolo12345)
You mind helping me on part c, although i dont think they are related. i got so much to learn for the exam in a few weeks @@@@@@@@@

Question is

ci) Given that is an acute angle and tan , show that

ii) Hence show that where p is a rational number

ii uses the double angle formula im guessing but i dont know what to do at all for part i)
I think I've seen this question before in one of my past papers.

First Part:
So you know that
Therefore we can conclude that:

So...

Then square both sides and it should be obvious.

Second Part:
We know and . So we can find
And remember:

Problem solved
15. (Original post by Wednesday Bass)
I think I've seen this question before in one of my past papers.

First Part:
So you know that
Therefore we can conclude that:

So...

Then square both sides and it should be obvious.

Second Part:
We know and . So we can find
And remember:

Problem solved
sorry must sound like an idiot but what do you get if you square

And just wondering the mark scheme seems to have a "shortcut answer" ... using pythagorous ... ?

and thanks perfectly understand part ii
16. (Original post by piccolo12345)
sorry must sound like an idiot but what do you get if you square

And just wondering the mark scheme seems to have a "shortcut answer" ... using pythagorous ... ?

and thanks perfectly understand part ii

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