# (Difficult) Trigonometry

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Yes, Gabzinc is asking for help once again. Sorry.

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!

Spoiler:

thats if you even know who I am

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thats if you even know who I am

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!

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#4

(Original post by

How is that difficult?

**Mr Moon Man**)How is that difficult?

If you're a GCSE student and are not familiar with these type of questions then this is definitely not easy.

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#5

(Original post by

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.

**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.

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#6

(Original post by

Oh, I didn't read that part, my bad.

**Mr Moon Man**)Oh, I didn't read that part, my bad.

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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?

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?

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#8

(Original post by

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?

**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?

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#9

**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?

.

Try that and see what happens. Post you working if you get stuck.

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(Original post by

You divided the wrong equation by . Try dividing this equation by :

.

Try that and see what happens. Post you working if you get stuck.

**notnek**)You divided the wrong equation by . Try dividing this equation by :

.

Try that and see what happens. Post you working if you get stuck.

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#11

**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 need to solve

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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

(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

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#13

(Original post by

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

**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

Can you see how to get from here:

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

to here:

tan x = -1

?

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(Original post by

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

?

**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

?

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

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#15

(Original post by

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

**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

Remember that .

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

Do you get how that works?

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#16

**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

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#17

**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

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.

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#18

(Original post by

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

**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

**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?

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(Original post by

...

**notnek**)...

(Original post by

...

**RDKGames**)...

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

You

**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.EDIT: Also, I want to give out more rep to everyone but I can't rep you guys multiple times in a row

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#20

(Original post by

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.

**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.

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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