# (Difficult) Trigonometry

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#1
Yes, Gabzinc is asking for help once again. Sorry.
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Having some difficulty with an entrance exam question which evidently has something to do with trigonometry. Can anybody offer clues as to the first step in working?

Here it is:

Thanks!
0
3 years ago
#2
divide each term by cosx....
1
3 years ago
#3
Divide by cos(x) then work out tan(x)= -1
0
3 years ago
#4
(Original post by Mr Moon Man)
How is that difficult?
It's simple for A Level but this is an entrance exam for a GCSE student.

If you're a GCSE student and are not familiar with these type of questions then this is definitely not easy.
3
3 years ago
#5
(Original post by notnek)
It's simple for A Level but this is an entrance exam for a GCSE student.

If you're not familiar with this type of question and haven't seen the identity before then this is definitely not easy.
0
3 years ago
#6
(Original post by Mr Moon Man)
don't think the op mentioned it anywhere on this thread anyway lol.
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#7
Thanks for the help so far guys, but I'm still a little confused :3

so dividing each side by cos x gives me:

tan x/cos x = sin x/cos^2 x

then using tan x = -1 gives me x= -45 (why do I do this?)

so both sides are equal to -root 2....

and then I'm lost. Sorry if I didn't make it clear, yes I'm a GCSE student. I don't understand this even with the new GCSE syllabus which has been made quite a bit harder :/

any more tips guys?
0
3 years ago
#8
(Original post by Gabzinc)
Thanks for the help so far guys, but I'm still a little confused :3

so dividing each side by cos x gives me:

tan x/cos x = sin x/cos^2 x

then using tan x = -1 gives me x= -45 (why do I do this?)

so both sides are equal to -root 2....

and then I'm lost. Sorry if I didn't make it clear, yes I'm a GCSE student. I don't understand this even with the new GCSE syllabus which has been made quite a bit harder :/

any more tips guys?
They meant , not the first equation
1
3 years ago
#9
(Original post by Gabzinc)
Thanks for the help so far guys, but I'm still a little confused :3

so dividing each side by cos x gives me:

tan x/cos x = sin x/cos^2 x

then using tan x = -1 gives me x= -45 (why do I do this?)

so both sides are equal to -root 2....

and then I'm lost. Sorry if I didn't make it clear, yes I'm a GCSE student. I don't understand this even with the new GCSE syllabus which has been made quite a bit harder :/

any more tips guys?
You divided the wrong equation by . Try dividing this equation by : .

Try that and see what happens. Post you working if you get stuck.
0
#10
Ohhh, right, will do. Doing the problem now:
1
3 years ago
#11
(Original post by Gabzinc)
Thanks for the help so far guys, but I'm still a little confused :3

so dividing each side by cos x gives me:

tan x/cos x = sin x/cos^2 x

then using tan x = -1 gives me x= -45 (why do I do this?)

so both sides are equal to -root 2....

and then I'm lost. Sorry if I didn't make it clear, yes I'm a GCSE student. I don't understand this even with the new GCSE syllabus which has been made quite a bit harder :/

any more tips guys?
No is what your given not what you need to solve.

you need to solve 0
#12
Riiiiiigghhht... making progress I guess?

(sin x + cos x)/cos x = 0, so sin x /cos x + cos x/ cos x = 0

if tan x = -1, x must be -45

sin -45 / cos -45 = -1

cos -45/ cos -45 must be equal to one as anything divided by itself is 1.

-1 + 1 = 0!

so one the values are -45,
then +180 to make it fit the range, right?

so 45 and 135 are the answers, right? i hope
0
3 years ago
#13
(Original post by Gabzinc)
Riiiiiigghhht... making progress I guess?

(sin x + cos x)/cos x = 0, so sin x /cos x + cos x/ cos x = 0

if tan x = -1, x must be -45

sin -45 / cos -45 = -1

cos -45/ cos -45 must be equal to one as anything divided by itself is 1.

-1 + 1 = 0!

so one the values are -45,
then +180 to make it fit the range, right?

so 45 and 135 are the answers, right? i hope
tan x = -1 is correct but I feel you've got that from another post and not derived it yourself. Let me know if I'm wrong.

Can you see how to get from here:

sin x /cos x + cos x/ cos x = 0

to here:

tan x = -1

?
0
#14
(Original post by notnek)
tan x = -1 is correct but I feel you've got that from another post and not derived it yourself. Let me know if I'm wrong.

Can you see how to get from here:

sin x /cos x + cos x/ cos x = 0

to here:

tan x = -1

?
Yeah, someone mentioned tan x = -1 so I just put -1 into inverse tan on my calculator. But admittedly I have no idea how to get tan x = -1 from (sin x+ cos x)/cos x

the worst bit is that there are questions like this all over the paper. If I can't do it while spending an hour on it at home, I won't be able to do it in the exam 0
3 years ago
#15
(Original post by Gabzinc)
Yeah, someone mentioned tan x = -1 so I just put -1 into inverse tan on my calculator. But admittedly I have no idea how to get tan x = -1 from (sin x+ cos x)/cos x

the worst bit is that there are questions like this all over the paper. If I can't do it while spending an hour on it at home, I won't be able to do it in the exam Do you know how to find least common multiples?

Remember that .

I can essentially say that for an example where x = 2, .

Do you get how that works?
0
3 years ago
#16
(Original post by Gabzinc)
Yeah, someone mentioned tan x = -1 so I just put -1 into inverse tan on my calculator. But admittedly I have no idea how to get tan x = -1 from (sin x+ cos x)/cos x

the worst bit is that there are questions like this all over the paper. If I can't do it while spending an hour on it at home, I won't be able to do it in the exam  Divide each term by , assuming  Then the first term becomes from the identity, and the second becomes 1, and the third is still 0.

So you're left with and rearrange for 0
3 years ago
#17
(Original post by Gabzinc)
Yeah, someone mentioned tan x = -1 so I just put -1 into inverse tan on my calculator. But admittedly I have no idea how to get tan x = -1 from (sin x+ cos x)/cos x

the worst bit is that there are questions like this all over the paper. If I can't do it while spending an hour on it at home, I won't be able to do it in the exam Try to ignore other people's working and do the question yourself.

So you got to this equation which is correct:

sin x /cos x + cos x/ cos x = 0

There are two terms in this equation and both of them can be changed/simplified.

sinx / cosx is ?

cosx / cosx is ?

Try this and again post your thoughts if you get stuck.
0
3 years ago
#18
(Original post by Gabzinc)
If I can't do it while spending an hour on it at home, I won't be able to do it in the exam You start off by spending an hour on it at home - doesn't mean these sort of things will always take you an hour at home to do; with practice and understanding you'll be able to do it a lot quicker.

Anywho: from you get Can you see why this is true? (rememember that )

Then, can you simplify this? If so, what do you get?
1
#19
(Original post by notnek)
...
(Original post by RDKGames)
...
omg. It was in my face the whole time and I STILL didn't see this?
HUGE FACEPALM MOMENT

At least now in exams I won't make the same fatal mistake.

so sin x/cos x = tan x (as given in the formula)

and cos x/ cos x = 1

tan x + 1 =0
tan x = -1
x= -45

I'm so upset that I did not recognise this earlier!

Thanks a whole lot guys, but I have just one remaining question: why would you divide (sin x+ cos x) by cos x in the first place? Just in case a similar question comes up in the future.

(Original post by Zacken)
You start off by spending an hour on it at home - doesn't mean these sort of things will always take you an hour at home to do; with practice and understanding you'll be able to do it a lot quicker.
True. I am also planning to practice a little but of A/AS Level trig to help with my understanding a little.

EDIT: Also, I want to give out more rep to everyone but I can't rep you guys multiple times in a row 0
3 years ago
#20
(Original post by Gabzinc)
omg. It was in my face the whole time and I STILL didn't see this?
HUGE FACEPALM MOMENT

At least now in exams I won't make the same fatal mistake.

so sin x/cos x = tan x (as given in the formula)

and cos x/ cos x = 1

tan x + 1 =0
tan x = -1
x= -45

I'm so upset that I did not recognise this earlier!

Thanks a whole lot guys, but I have just one remaining question: why would you divide (sin x+ cos x) by cos x in the first place? Just in case a similar question comes up in the future.
Glad to help You divide by cosine because then you have an identity you can use, it's just a decision made by inspecting the equation for long enough. It helps because then you simplify your equation down to a single variable of for which you can solve.

But, er, while is true for the equation to hold, it is not a valid solution for this question because the range for it is . Are you able to hack around this one??
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