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Maths trigonometry

PQR is a right angle triangle. QS is perpendicular to PR, and PQ has length 1.

1) Find QS and PS in-terms of 0.


2) By considering triangle QSR, find an expression for SR.

3) By considering triangle PQR, find PR in-terms of e.

4) Hence, show that
cos A = sec 0 -sin o tan 0.


Some one please help me I'm stuck on this question.
(edited 3 years ago)

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Original post by Omarblack
PQR is a right angle triangle. QS is perpendicular to PR, and PQ has length 1.

1) Find QS and PS in-terms of 0.

2) By considering triangle QSR, find an expression for SR.

3) By considering triangle PQR, find PR in-terms of e.

4) Hence, show that
cos A = sec 0 -sin o tan 0.

Post your working so far
Reply 2
Here is my workings out so far but not sure if it's right and I'm stuck. 16031966414493125698962960414339.jpg
Reply 3
Original post by Muttley79
Post your working so far

I have.
Original post by Omarblack
I have.

OK I'll take a look - this wasn't there when I replied :smile:
Reply 5
Original post by Muttley79
OK I'll take a look - this wasn't there when I replied :smile:

OK, thank you very much
Original post by Omarblack
OK, thank you very much

OK I go the result - you need to rewrite what you have:

QS =

PS =

SR =

PR = PS + SR .... then rearrange
Reply 7
What do you mean by rewrite?

Do you mean make it equal to PS and RS and SR in the separate questions?

What do you mean by rewrite?

Do you mean make it equal to PS and RS and SR in the separate questions?
Original post by Omarblack
What do you mean by rewrite?

Do you mean make it equal to PS and RS and SR in the separate questions?

What do you mean by rewrite?

Do you mean make it equal to PS and RS and SR in the separate questions?

You need to quote me so I can see you've responded.

Follow the question through as it asks. You get expressions for all these lengths.

Then put them together at the end: expression for PR = PS + SR

Write out as I suggested:

sin theta = QS/1 so QS =

tan theta =

No need to use Pythag as we know angle SQR = theta as well
Reply 9
Original post by Muttley79
OK I go the result - you need to rewrite what you have:

QS =

PS =

SR =

PR = PS + SR .... then rearrange

16031993411618381433785848602767.jpg
This is what I've got?
Original post by Omarblack

This is what I've got?

See my hint about QS ...
Reply 11
Original post by Muttley79
You need to quote me so I can see you've responded.

Follow the question through as it asks. You get expressions for all these lengths.

Then put them together at the end: expression for PR = PS + SR

Write out as I suggested:

sin theta = QS/1 so QS =

tan theta =

No need to use Pythag as we know angle SQR = theta as well


Original post by Muttley79
See my hint about QS ...

I think I'm following, so what you mean is since

sine (pheta) = 1/QS Then QS = tan(pheta) but after that point I'm lost because surely PS = QS / tan (pheta) so doesn't that mean QS would rearrange to PStan(pheta)
Also tan is sine/cos. So I'm really confused now. If we was following the the expressions and rearranging as we go then I must be doing something wrong in my workings out, but I don't know what it is.
Original post by Omarblack
I think I'm following, so what you mean is since

sine (pheta) = 1/QS Then QS = tan(pheta) but after that point I'm lost because surely PS = QS / tan (pheta) so doesn't that mean QS would rearrange to PStan(pheta)
Also tan is sine/cos. So I'm really confused now. If we was following the the expressions and rearranging as we go then I must be doing something wrong in my workings out, but I don't know what it is.

sin theta = opp/hyp = QS/1

tan theta = QS/PS so PS =QS/tan theta now sub in QS

Sorry back later ... need to go
Reply 13
Original post by Muttley79
sin theta = opp/hyp = QS/1

tan theta = QS/PS so PS =QS/tan theta now sub in QS

Sorry back later ... need to go

When you see this, I think I understand.

Since sine(pheta) = QS/1 THEN QS = SINE(PHETA)

and PS = QS/TAN(PHETA).

I'M STILL PUZZLED ON THE REST THOUGH.
Original post by Omarblack
When you see this, I think I understand.

Since sine(pheta) = QS/1 THEN QS = SINE(PHETA)

and PS = QS/TAN(PHETA).

I'M STILL PUZZLED ON THE REST THOUGH.

Sub in QS and the start on the second triangle ... post what you get .. don't give up
Reply 15
Original post by Muttley79
Sub in QS and the start on the second triangle ... post what you get .. don't give up

OK thanks for the guidance so far. This is my current results for the expression for SR.

Is this correct? If it is could you give me some guidance for the whole triangle please?

16032048870108548866454690370744.jpg
Original post by Omarblack
OK thanks for the guidance so far. This is my current results for the expression for SR.

Is this correct? If it is could you give me some guidance for the whole triangle please?


Now put it all together:
PR = PS + SR

What did you have for PR and PS? I agree with SR
Reply 17
Original post by Muttley79
Now put it all together:
PR = PS + SR

What did you have for PR and PS? I agree with SR

I get QS/tan(pheta) + sin(pheta) tan(pheta) is this correct?
Original post by Omarblack
I get QS/tan(pheta) + sin(pheta) tan(pheta) is this correct?

You know QS = sin theta so simplify that.

Now put = PR
Reply 19
Original post by Muttley79
You know QS = sin theta so simplify that.

Now put = PR

After Simplification I have cos(pheta) sin(pheta) + sim(pheta) tan(pheta)?

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