Universecolors
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Image of question is below. Any help is appreciated.
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Universecolors
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mqb2766
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#3
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Just use the normal formula for cos and remember its in a negative quadrant
The hypotenuse is easy to work out using pythagoras.
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hoosie
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mqb2766
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(Original post by hoosie)
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Pls read the sticky at the top of the forum about answering questions, in particular
"If a hint has already been given, please do not offer a bigger hint."
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hoosie
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(Original post by mqb2766)
Pls read the sticky at the top of the forum about answering questions, in particular
"If a hint has already been given, please do not offer a bigger hint."
I believe a better (not bigger hint) should be provided if my judgement is that the first hint is not the best approach for the student to take. I thought in this case mentioning that the question is based on the unit circle is critical to a student’s understanding of the question. Your suggestion to the OP that they use Pythagoras to work out the hypotenuse completely misses the point of the question. It should be obvious that the radius of the unit circle is 1 unit. My question about how cosβ (Q1) relates to cosβ (Q3) encourages the OP to think about how they can find an answer to cosθ (taking into account it’s sign). No calculation is required - just observation of the circle diagram.
Last edited by hoosie; 9 months ago
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mqb2766
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(Original post by hoosie)
I believe a better (not bigger hint) should be provided if my judgement is that the first hint is not the best approach for the student to take. I thought in this case mentioning that the question is based on the unit circle is critical to a student’s understanding of the question. Your suggestion to the OP that they use Pythagoras to work out the hypotenuse completely misses the point of the question. It should be obvious that the radius of the unit circle is 1 unit. My question about how cosβ (Q1) relates to cosβ (Q3) encourages the OP to think about how they can find an answer to cosθ (taking into account it’s sign). No calculation is required - just observation of the circle diagram.
You're making assumptions about me/my response which are not correct and I'm not going to argue about.
Please observe the guidelines in the sticky as mentioned in the previous post, rather than making assumptions.
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old_engineer
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(Original post by hoosie)
I believe a better (not bigger hint) should be provided if my judgement is that the first hint is not the best approach for the student to take. I thought in this case mentioning that the question is based on the unit circle is critical to a student’s understanding of the question. Your suggestion to the OP that they use Pythagoras to work out the hypotenuse completely misses the point of the question. It should be obvious that the radius of the unit circle is 1 unit. My question about how cosβ (Q1) relates to cosβ (Q3) encourages the OP to think about how they can find an answer to cosθ (taking into account it’s sign). No calculation is required - just observation of the circle diagram.
I'm with mqb2766 here. As well as disregarding "If a hint has already been given, please do not offer a bigger hint" you have also disregarded "Do not "barge in" while another helper is offering hints".
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RogerOxon
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(Original post by hoosie)
It should be obvious that the radius of the unit circle is 1 unit.
How is it "obvious" that it's a unit circle?

Unless it's explicitly stated, it's dangerous to assume it, rather than make the (easy) calculation.
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hoosie
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(Original post by old_engineer)
I'm with mqb2766 here. As well as disregarding "If a hint has already been given, please do not offer a bigger hint" you have also disregarded "Do not "barge in" while another helper is offering hints".
I don’t believe advising the OP to calculate the hypotenuse using Pythagoras is the correct approach in this instance and so I provided an alternative approach to help the student gain a complete understanding of the question. I believe it is important for a student to be offered alternative approaches to answering questions and so offering a hint along a different line is not barging in when the first hint relates to a different method to answering the question. The first approach makes no mention of the unit circle which the question is based on. I certainly agree that a bigger hint should not be given if a hint has already been provided by someone, provided both hints are using the same approach. If as this case a different approach is taken then a first hint for the alternative method, I believe, is valid and necesssary for the benefit of the student.
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hoosie
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(Original post by RogerOxon)
How is it "obvious" that it's a unit circle?

Unless it's explicitly stated, it's dangerous to assume it, rather than make the (easy) calculation.
I didn’t say it’s obvious that it’s a unit circle. I said it’s obvious the radius of a unit circle is one unit. Many years teaching Trigonometry tells me that questions like this are based on the knowledge of this circle.This problem is testing a student’s knowledge of the first quadrant of a unit circle and how it relates to the third quadrant. The student should be encouraged to read the cosine answer directly from the diagram as an alternative approach to calculating the hypotenuse. Most importantly if the OP can understand both approaches and how they relate to each other that’s better for their overall understanding.
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mqb2766
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(Original post by hoosie)
I don’t believe advising the OP to calculate the hypotenuse using Pythagoras is the correct approach in this instance and so I provided an alternative approach to help the student gain a complete understanding of the question. I believe it is important for a student to be offered alternative approaches to answering questions and so offering a hint along a different line is not barging in when the first hint relates to a different method to answering the question. The first approach makes no mention of the unit circle which the question is based on. I certainly agree that a bigger hint should not be given if a hint has already been provided by someone, provided both hints are using the same approach. If as this case a different approach is taken then a first hint for the alternative method, I believe, is valid and necesssary for the benefit of the student.
Using pythagoras - its "obviously" a unit circle, however some people won't spot it. Rather than telling the person the answer, I encouraged them to calculate it. Yours was not an alternative approach.

For the benefit of the student, the sticky says to offer just enough hints. The original response did that.
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Universecolors
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#13
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(Original post by hoosie)
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Thank you , that helps a lot !
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