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# A quick tan clarification question??? (1 mark)

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1. Here it is attached.

I know from the calculator tan-1(0.75) = 36.9 degrees

The marks scheme says

"There is a second angle in the third quadrant, where
the cos value is negative
i.e. x = 180 + 36.9 = 216.90"

How did they know their was a second angle in third quadrant?

Thanks
2. (Original post by blueray)
Here it is attached.

I know from the calculator tan-1(0.75) = 36.9 degrees

The marks scheme says

"There is a second angle in the third quadrant, where
the cos value is negative
i.e. x = 180 + 36.9 = 216.90"

How did they know their was a second angle in third quadrant?

Thanks
Have you ever used the CAST diagram?
3. Just find both answers for cos and both answers for tan and then find which answer appears in both lists.
4. (Original post by blueray)
Here it is attached.

I know from the calculator tan-1(0.75) = 36.9 degrees

The marks scheme says

"There is a second angle in the third quadrant, where
the cos value is negative
i.e. x = 180 + 36.9 = 216.90"

How did they know their was a second angle in third quadrant?

Thanks
Use the C A S T diagram
5. (Original post by SilentIdea)
Have you ever used the CAST diagram?
Yes I know what it is and how it works

But how would I know to select the 3rd quadrent? |That's the part I dont get.
6. (Original post by blueray)
Yes I know what it is and how it works

But how would I know to select the 3rd quadrent? |That's the part I dont get.
7. (Original post by SilentIdea)
But I don't understand how that's related to "cos" it's asking to satisfy cos x =-0.8 as well.
8. (Original post by blueray)
But I don't understand how that's related to "cos" it's asking to satisfy cos x =-0.8 as well.

You would use the A and C quadrants. A is where they are all positive and C is where Cos is positive.

If it happened to be negative then you would use S and T as that's where Cos is negative.

Looking at your answers of x for tan and cos, the ones that are in both are the answers.
9. (Original post by SilentIdea)

You would use the A and C quadrants. A is where they are all positive and C is where Cos is positive.

If it happened to be negative then you would use S and T as that's where Cos is negative.
Ok I understand that. But it doesn't use S in the answer. It only uses T why is that?
10. (Original post by blueray)
Ok I understand that. But it doesn't use S in the answer. It only uses T why is that?
Well working out Tan^-1(0.75), we get a positive answer. Looking at our CAST diagram we would now look in the A and T sections.

Working out Cos^-1(-0.8), we also get a positive answer. We now look in the A and C sections.

You should then have 2 angles from tan and 2 from cos. Which angle comes up in both?
11. (Original post by SilentIdea)
Well working out Tan^-1(0.75), we get a positive answer. Looking at our CAST diagram we would now look in the A and T sections.

Working out Cos^-1(-0.8), we also get a positive answer. We now look in the A and C sections.

You should then have 2 angles from tan and 2 from cos. Which angle comes up in both?
I have 2 angles as I know it can be in ALL and COS

but I don't know which angle comes up in both
12. (Original post by blueray)
I have 2 angles as I know it can be in ALL and COS

but I don't know which angle comes up in both
13. (Original post by b_white)
Can't you do

0<x<360

tan x = 0.75 = (sin x)/(cos x)
cos x = -0.8

sin x = 0.75 * -0.8

then just get the two values of x from that?
Umm I don't think so. When doing sin^-1(-0.6), i get a negative answer. I have to now look in the T and C sections. This gives me two answers. I need one value of x.
14. (Original post by SilentIdea)
36.9 and
180 - 36.9 = 143.1

I have these 2....now what???
15. (Original post by blueray)
36.9 and
180 - 36.9 = 143.1

I have these 2....now what???
Are those the two angles for Tan? If so move onto Cos. EDIT: Check your second angle for Tan again. It should be in the 3rd quadrant remember.
16. (Original post by SilentIdea)
Are those the two angles for Tan? If so move onto Cos.
No you said look at A and T so I will have to do it again

T is 36.9

A is??? What is A how do I work it out?

Please can you explain the answer now, I really don't have time
17. (Original post by blueray)
36.9 and
180 - 36.9 = 143.1

I have these 2....now what???
Those are not the two angles for tan.

The first angle is 36.9 and is in the first quadrant where tan is positive. Tan is also positive in the 3rd quadrant so to get an angle in the third quadrant do 180 +36.9 which gives you 216.9

Therefore values of tan are 216.9 and 36.9
18. (Original post by GreenLantern1)
Those are not the two angles for tan.

The first angle is 36.9 and is in the first quadrant where tan is positive. Tan is also positive in the 3rd quadrant so to get an angle in the third quadrant do 180 +36.9 which gives you 216.9

Therefore values of tan are 216.9 and 36.9
I just meant the angles you get for Tan when looking in the first and third quadrant.
19. (Original post by SilentIdea)
I just meant the angles you get for Tan when looking in the first and third quadrant.
That is exactly what I put lol, I don't get your query!
20. (Original post by GreenLantern1)
That is exactly what I put lol, I don't get your query!
Oh, I misread it. I thought you said there are not two angles for Tan. My bad.

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