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# Maths C3 - Trigonometry... Help??

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1. (Original post by ValerieKR)
simplify cos(x)sec(x) and put the remaining terms over a cos(x) denominator
Thank you soooooo much!! I managed to work it out now. Yayyyyy.
2. Another few of my silly questions...

Positive in the 1st and 2nd quadrant --- Negative in the 3rd and 4th quadrant
Positive in the 1st and 4th --- Negative in the 2nd and 3rd
Postive in the 1st and 3rd --- Negative in the 2nd and 4th
???

Q2) How come...

...the square root makes cos positive and negative but...

...with the cube root in this equation tan just remains positive??

I know that square roots can are +/- but does the same not apply to cube roots?

Sorry for the ridiculously silly questions
3. (Original post by Philip-flop)
...
If the original question was then you get so you get two different trig equations to solve.

But with , cube rooting gives only which is only one trig equation to solve. I'm not really sure what you're asking tbh, could you post the original question and your working out?
4. (Original post by Philip-flop)

I know that square roots can are +/- but does the same not apply to cube roots?
Sorry for the ridiculously silly questions

Nope.

Take -1 for instance. Squaring it, or raising it to any even power, will give the result of +1. This is also the case for the number +1 itself, if you raise it to any even power.

If you were to cube -1, then you would be multiplying it by itself 3 times and you come back to -1 again. Same with any odd power. Now if you apply odd powers to the number +1, then you would just come back to +1 again.

So; for even powers, all numbers go positive; hence +/- solutions for any equations with square roots. For odd powers, negatives stay negative, and positives stay positive. Therefore odd roots of a negative will be negative, and odd roots of a positive are positive. Hence no +/- in the answer.
5. (Original post by Zacken)
could you post the original question and your working out?
Taken from the Edexcel C3 Modular Maths Textbook - Exercise 6C Questions: 5(e) and 5(g)

Solve, for the values of in the interval
...

Q5(e)

Q5(g)
Attachment 580138580140
Attached Images

6. (Original post by RDKGames)
Nope.

Take -1 for instance. Squaring it, or raising it to any even power, will give the result of +1. This is also the case for the number +1 itself, if you raise it to any even power.

If you were to cube -1, then you would be multiplying it by itself 3 times and you come back to -1 again. Same with any odd power. Now if you apply odd powers to the number +1, then you would just come back to +1 again.

So; for even powers, all numbers go positive; hence +/- solutions for any equations with square roots. For odd powers, negatives stay negative, and positives stay positive. Therefore odd roots of a negative will be negative, and odd roots of a positive are positive. Hence no +/- in the answer.
Oh yeah!! That's it! Thank you so much. I don't know why but I seem to know these things already but when it comes to applying it to questions I panic and forget simple things like that.

Great explanation. It makes perfect sense now.
7. (Original post by Philip-flop)
Taken from the Edexcel C3 Modular Maths Textbook - Exercise 6C Questions: 5(e) and 5(g)

Solve, for the values of in the interval
A bit messy.

So you have so since you take reciprocals of both sides.

At which point

Your tan looks good but it would just be easier to rewrite cube root of 1/8 as 1/2.

Also I think learning and remembering the general solutions of trigonometric functions in FP1 can make it so much neater for you to solve these types in C3. It's a really short topic, look at it if you can. I feel like the quadrant thing just leaves much more room for error.
8. (Original post by RDKGames)
9. (Original post by RDKGames)
A bit messy.

So you have so since you take reciprocals of both sides.

At which point

Your tan looks good but it would just be easier to rewrite cube root of 1/8 as 1/2.

Also I think learning and remembering the general solutions of trigonometric functions in FP1 can make it so much neater for you to solve these types in C3. It's a really short topic, look at it if you can. I feel like the quadrant thing just leaves much more room for error.
Oh yeah. I didn't think of just taking the reciprocal of both sides since.. sec is the reciprocal of cos

This is why I will never be goood at Maths
10. Ok, here I go again...

Solve, for the values of in the interval

How do I even solve this equation?...

11. (Original post by Philip-flop)
Ok, here I go again...

Solve, for the values of in the interval

How do I even solve this equation?...

Rewrite cot in terms of sin and cos. Get sine squared, get cos squared from that. Boom you got a quadratic in terms of cos.
12. (Original post by RDKGames)
Rewrite cot in terms of sin and cos. Get sine squared, get cos squared from that. Boom you got a quadratic in terms of cos.
Ok so I'm up to...

how do I get cos squared from that?
13. (Original post by Philip-flop)
Ok so I'm up to...

how do I get cos squared from that?
14. (Original post by RDKGames)
I'm not sure I can see where to use that trig identity for

Edit: wait yeah I can see it!! I was being silly
15. (Original post by RDKGames)
Thanks again!! I just needed prompting for that equation

I managed to get...

Seriously appreciate your help. Sorry I'm such a pest
16. (Original post by Philip-flop)
Thanks again!! I just needed prompting for that equation

I managed to get...

Seriously appreciate your help. Sorry I'm such a pest
Yeah that's correct, not a pest . So now

or

17. ^Do I start off by using the quadratic formula on this?

Or shall I use the Trig rule ...
18. (Original post by Philip-flop)

^Do I start off by factorising this?
Yeah. Or completing the square.
19. (Original post by RDKGames)
Yeah. Or completing the square.
Or shall I use the Trig rule ... ??
20. (Original post by Philip-flop)
Or shall I use the Trig rule ... ??
No need, the quadratic is all in terms of a single unknown variable and that's as simple as it gets.

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