Determine the value of x, in simplest exact form.

I

indifferentbear

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Hello everyone,

I was wondering if anyone could help me out with this question.

Determine a value of x, give answer in simplest exact form.

sin(8pi/23)=sinx

x is not equal to 8pi/23

To be honest im not even sure what the question is asking. Is it asking me to find another value of x which will satisfy the problem?

I cant find a way to use special triangles and the compound angle formulas are not helping me either.

I would be very grateful for any help given!
 
indifferentbear said:
Hello everyone,

I was wondering if anyone could help me out with this question.

Determine a value of x, give answer in simplest exact form.

sin(8pi/23)=sinx

x is not equal to 8pi/23

To be honest im not even sure what the question is asking. Is it asking me to find another value of x which will satisfy the problem?

I cant find a way to use special triangles and the compound angle formulas are not helping me either.

I would be very grateful for any help given!
Click to expand...
Hint: sin(\(\displaystyle \theta \)) = sin(\(\displaystyle \pi - \theta \))

Please show us what you have tried and exactly where you are stuck.​
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Please share your work/thoughts about this assignment.​
 
Apologies,

My working so far:
sin8pi/23 = sinx

sinx = sin (x+2pi)

sin 8pi/23 = sin (x+2pi)

= sin (8pi/23 + 2pi)

= sin(8pi/23 + 46pi/23)

= sin (54pi/23)

I'm not sure if the questions is asking for an equivalent value of x?

If this is the case then surely you could just multiply 8pi/23 by any number and get 8pi/23 is not equal to x?


Thanks so much
 
Jomo said:
How is your instructor interpreting simplest form?
Click to expand...

So this is why I am confused.

No other question has been structured this way whilst learning.

I can find the exact value of a radian/degree value and find value of theta. I am also confident with compound angle formula and proving identities.

I'm just not sure what this question is asking me.
 
Can you please post a photo-copy of your assignment?
 
indifferentbear said:
Determine a value of x, give answer in simplest exact form.

sin(8pi/23)=sinx

x is not equal to 8pi/23

To be honest im not even sure what the question is asking. Is it asking me to find another value of x which will satisfy the problem?
Click to expand...
I would expect this to mean that you are to give all solutions, not just one.

The fact is that x could be equal to 8pi/23; or it could equal an angle in the second quadrant; or it could be any coterminal angle. So your answer should have the form "____ or ____", where either option yields infinitely many numbers, for any integer value of some parameter (k, n, or whatever is usual in your class). You gave an example of one coterminal angle; how can you represent all of them?

On the other hand, if it literally says what you show, "determine a value", and specifies that your value of x can't be 8pi/23, then your answer in post #3 is a valid answer. (I initially took that as just saying your were told you were wrong in saying it was 8pi/23.)
 
Dr.Peterson said:
I would expect this to mean that you are to give all solutions, not just one.

The fact is that x could be equal to 8pi/23; or it could equal an angle in the second quadrant; or it could be any coterminal angle. So your answer should have the form "____ or ____", where either option yields infinitely many numbers, for any integer value of some parameter (k, n, or whatever is usual in your class). You gave an example of one coterminal angle; how can you represent all of them?

On the other hand, if it literally says what you show, "determine a value", and specifies that your value of x can't be 8pi/23, then your answer in post #3 is a valid answer. (I initially took that as just saying your were told you were wrong in saying it was 8pi/23.)
Click to expand...

Thank you for your time. Yeah, I am very confused as every other question I have come across is clear on what it is asking of you.
 
I re-read the problem. It asked to find a value for x (except 8pi/23). I would just add 2pi (or 4pi or 6pi,....or -2pi, -4pi,....) clean up the answer and be done.
 
Jomo said:
I re-read the problem. It asked to find a value for x (except 8pi/23). I would just add 2pi (or 4pi or 6pi,....or -2pi, -4pi,....) clean up the answer and be done.
Click to expand...
Yes, seeing the problem as actually written, I think it is reasonably clear if you know how to read a math problem carefully (which should probably not be assumed of all students ...). The answer in #3 is indeed fully appropriate.

The hard part is that students commonly are used to having only one correct answer, and are confused when they have to make an arbitrary choice. I used to be bothered when students turned in homework problems with the answer "Answers may vary", until I stopped assigning problems with answers in the back of the book.
 
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