Finding value of cos t within an interval

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KingRich
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Okay, I’m not sure why but when working with degrees. It seems a lot more simpler when using its identities to find the following x within the interval.

I must be inputting on the calculator wrong.

I know that cos x = cos-x = cos x+360…

I believe I’ve applied correctly based on the graph.

However, when I for example do cos(x+360) I’m getting a value 0.898 which is between the interval asked.

My calculator is set to degrees too but my text book states that it’s wrong. Can someone confirm this please?

Also, any idea what I could be doing wrong?

Edit: ignore the 0.644. I found this answer when my calculator was set to radians, although I now realise this is not degrees

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Last edited by KingRich; 4 weeks ago
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mqb2766
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Are you sorted or is there still something wrong?
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adam.jmg04
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(Original post by KingRich)
Okay, I’m not sure why but when working with degrees. It seems a lot more simpler when using its identities to find the following x within the interval.

I must be inputting on the calculator wrong.

I know that cos x = cos-x = cos x+360…

I believe I’ve applied correctly based on the graph.

However, when I for example do cos(x+360) I’m getting a value 0.898 which is between the interval asked.

My calculator is set to degrees too but my text book states that it’s wrong. Can someone confirm this please?

Also, any idea what I could be doing wrong?

Edit: ignore the 0.644. I found this answer when my calculator was set to radians, although I now realise this is not degrees

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Views: 9
Size:  75.1 KB
when the range is given in radians, set your calculator to radians. so you will do cos^-1 (4/5) which will give you 0.64...

as your range is between 0 and 4𝜋, and it is a cos graph, your values will be: 0.64 , (2𝜋 - 0.64), (2𝜋 + 0.64), (4𝜋 - 0.64). I can draw a diagram to explain if necessary

I think on your diagram you have plotted 0.64 on the wrong axis as this is the angle in radians so it must be on the x axis, and 4/5 will be on the y axis. And you might have gotten confused about this, try to stay in radians if the question is asking for radians. Same for degrees. You will get used to it over time. Took me a while to wrap my head around this topic.
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KingRich
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(Original post by adam.jmg04)
when the range is given in radians, set your calculator to radians. so you will do cos^-1 (4/5) which will give you 0.64...

as your range is between 0 and 4𝜋, and it is a cos graph, your values will be: 0.64 , (2𝜋 - 0.64), (2𝜋 + 0.64), (4𝜋 - 0.64). I can draw a diagram to explain if necessary

I think on your diagram you have plotted 0.64 on the wrong axis as this is the angle in radians so it must be on the x axis, and 4/5 will be on the y axis. And you might have gotten confused about this, try to stay in radians if the question is asking for radians. Same for degrees. You will get used to it over time. Took me a while to wrap my head around this topic.
That makes me feel a little better, not being the only one who found it confusing lol.

I have attempted the question based on degrees that I have done originally. Perhaps, you can confirm this for me to see if my basics is correct.

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tbh, I’m not sure what the 0.64 represents when it’s in radians.

So,
1. Keep in radians unit

if working from the unit graph. What would 0.64 be? I assume it would be the length of the base triangle?

I can confirm my calculator is set in radians and I have tried your method to find 0.799 for one of the values. Mmm, it could be the text book that’s wrong again.

the values are 0.644,5.64,6.93 and 11.9

Edit: sorry, I included cos within the calculations.

I finally got there and found the same results as given.

Thank you
Last edited by KingRich; 4 weeks ago
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adam.jmg04
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(Original post by KingRich)
That makes me feel a little better, not being the only one who found it confusing lol.

I have attempted the question based on degrees that I have done originally. Perhaps, you can confirm this for me to see if my basics is correct.

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tbh, I’m not sure what the 0.64 represents when it’s in radians.

So,
1. Keep in radians unit

if working from the unit graph. What would 0.64 be? I assume it would be the length of the base triangle?

I can confirm my calculator is set in radians and I have tried your method to find 0.799 for one of the values. Mmm, it could be the text book that’s wrong again.

the values are 0.644,5.64,6.93 and 11.9

Edit: sorry, I included cos within the calculations.

I finally got there and found the same results as given.

Thank you
Your answers are right in terms of degrees (multiply them by 𝜋/180 to convert from degrees to radians, divide by 𝜋/180 for conversion from radians to degrees). But remember that they will only accept the answer in radians so pay close attention to what it is asking. You would not get full marks for that solution, but you probably knew this!

Well done for getting them in radians too! I'm guessing you understand it now or is there anything else that is unclear?
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KingRich
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#6
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#6
(Original post by adam.jmg04)
Your answers are right in terms of degrees (multiply them by 𝜋/180 to convert from degrees to radians, divide by 𝜋/180 for conversion from radians to degrees). But remember that they will only accept the answer in radians so pay close attention to what it is asking. You would not get full marks for that solution, but you probably knew this!

Well done for getting them in radians too! I'm guessing you understand it now or is there anything else that is unclear?
Yes, I believe it all makes sense now and finding the radians is straightforward.

the question asked for the answers to three significant figures and hence the answers above. I forgot to mention that in the original question.

This is why I confused more than anything I think because I’ve not come across a question like this as I’m always asked to solve in degrees or radians.
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KingRich
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#7
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#7
(Original post by mqb2766)
Are you sorted or is there still something wrong?
All sorted now thanks
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