C4 Trig help

Have you been taught the ASTC square method? Something like this:

Show some working and we'll be able to see where you've gone wrong.

Reply 3

Original post by Jacklicy

Solve the equation 2cosx - 5sinx = 3 for 0°≤ x ≤ 360°

I've already put it in the form Rcos(x+a), where √29 cos (x + 68.2) = 3

However I do not understand how to find out the two values of x. According to the MEI books the answer is 235.7 and 347.9.

Could someone please explain how to get to the two answers with using the cos graph? Thanks a ton!

You asked this question already....did u not get it in the other post...?

Reply 4

OP

Original post by tory88

Have you been taught the ASTC square method? Something like this:

Show some working and we'll be able to see where you've gone wrong.

Here are my working outs from the start.
2cosx - 5sinx = 3 for 0°≤ x ≤ 360°
Rcos(x+a) = (Rcosa)cosx + (Rsina)sinx

So Rcosa = 2, R sina = 5.
R = √4+25 = √29
a = Tan-1(5/2) = 68.2

Therefore √29cos(x+68.2) = 3

x+68.2 = cos-1(3/√29)
x = 56.1 - 68.2 = -12.1

This is what I've got so far. I believe it is wrong though. And also I believe I've heard of the CAST diagram, but we didn't get taught how to use it.

(edited 11 years ago)

Reply 5

OP

Original post by 2710

You asked this question already....did u not get it in the other post...?

This is a new question I came across. This one is harder than the last one since I followed your method of using the cos graph but still couldn't get the correct answer for this one :s-smilie:

Reply 6

Anythingoo1

13

Original post by Jacklicy

Here are my working outs from the start.
2cosx - 5sinx = 3 for 0°≤ x ≤ 360°
Rcos(x+a) = (Rcosa)cosx + (Rsina)sinx

So Rcosa = 2, R sina = 5.
R = √4+25 = √29
a = Tan-1(5/2) = 68.2

Therefore √29cos(x+68.2) = 3

x+68.2 = cos-1(3/√29)
x = 56.1 - 68.2 = -12.1

This is what I've got so far. I believe it is wrong though.

use Sin(a-x) = (Rsina)cosx - (Rcosa)sinx or alternatively -(Sin(x-a)) = (Rsina)cosx - (Rcosa)sinx

Make sure you get the right angles from the formula sheet, don't mix them up

Your working seems ok to me, try my suggestion and it should iron out the mistakes in your question

Reply 7

OP

Original post by Anythingoo1

use Sin(a-x) = (Rsina)cosx - (Rcosa)sinx or alternatively -(Sin(x-a)) = (Rsina)cosx - (Rcosa)sinx

Make sure you get the right angles from the formula sheet, don't mix them up

Your working seems ok to me, try my suggestion and it should iron out the mistakes in your question

I've tried your method.

Ended up with √29sin(x+68.2) = 3.
And x+68.2 = sin-1(3/√29)
x = -34.3

Still no luck :/

Reply 8

Original post by Jacklicy

This is a new question I came across. This one is harder than the last one since I followed your method of using the cos graph but still couldn't get the correct answer for this one :s-smilie:

Its not harder. Its the exact same question with different numbers.

cos^-1(3/√29) gives you two answers. The first, is 56.1 by calculator. So look at the cos graph. Look at the symmetry. Which other also gives you the same answer? You can see 360 - 56.1 also gives you the answer

Reply 9

OP

Original post by 2710

Its not harder. Its the exact same question with different numbers.

cos^-1(3/√29) gives you two answers. The first, is 56.1 by calculator. So look at the cos graph. Look at the symmetry. Which other also gives you the same answer? You can see 360 - 56.1 also gives you the answer

The answer given by the book was 235.7 and 347.9, which didn't make sense when I followed your method. I understand your method and how to use the cos graph, but where the 347.9 comes from just puzzles me.

Reply 10

Original post by Jacklicy

The answer given by the book was 235.7 and 347.9, which didn't make sense when I followed your method. I understand your method and how to use the cos graph, but where the 347.9 comes from just puzzles me.

This is 360 - 12.1

You have -12.1 originally right? This is a correct answer, but not in the range. So just look at the cos graph. Cos(-12.1) = cos(360-12.1)

So think like this:

x+68.2 = cos^-1(3/√29)

The two preliminary solutions are x+68.2 = 56.1 and 360-56.1 (by graph)

But you know 56.1 will give you an out of range answer wen you minus 68.2 from it. So to resolve this...just add 360 to it. Because adding 360 to any number just gives you the same number, in terms of trigonometric functions. So now the two solutions you have are:

56.1+360 and 360-56.1

Then just minus your 68.2 to give you your final solutions

(edited 11 years ago)

Reply 11

OP

Oh I see now, thank you so much!

So the final answers are 56.1, 235.7 and 347.9 (-12.1 out of range so it doesn't need to be included) right? I'm guessing the mark scheme missed out 56.1 as an answer?

Reply 12