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Math Help - trigonometric concepts

  1. #1
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    trigonometric concepts

    Reading this, something rings in my mind, but I cant find the room the ring comes from I did this last year, but since I took an online class and therefor have no teacher,it's difficult to get the infos. The only thing I can remember is how to calculate sin,cos,tan using a scientific calculator

    Mrs. Imconfused is having difficulty understanding the trigonometric concepts. She doesn't know when to use the Primary Trigonometric Ratios (sin, cos and tan), the Sine Law or the Cosine Law. She also needs clarification on what each one (primary trig ratios, sine law, cosine law) can be used to calculate. Provide an explanation that will help to solidify her understanding. Be sure to discuss what each one will calculate and how to decide which one to use. Explanations, diagrams, examples, formulas and mathematical terminology should all be included in your solution. Be thorough!
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  2. #2
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    Quote Originally Posted by Serialkisser View Post
    Reading this, something rings in my mind, but I cant find the room the ring comes from I did this last year, but since I took an online class and therefor have no teacher,it's difficult to get the infos. The only thing I can remember is how to calculate sin,cos,tan using a scientific calculator

    Mrs. Imconfused is having difficulty understanding the trigonometric concepts. She doesn't know when to use the Primary Trigonometric Ratios (sin, cos and tan), the Sine Law or the Cosine Law. She also needs clarification on what each one (primary trig ratios, sine law, cosine law) can be used to calculate. Provide an explanation that will help to solidify her understanding. Be sure to discuss what each one will calculate and how to decide which one to use. Explanations, diagrams, examples, formulas and mathematical terminology should all be included in your solution. Be thorough!
    When in doubt, check Wikipedia

    Trigonometry - Wikipedia, the free encyclopedia
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  3. #3
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    Trigonometry

    Hello Serialkisser
    Quote Originally Posted by Serialkisser View Post
    Mrs. Imconfused is having difficulty understanding the trigonometric concepts. She doesn't know when to use the Primary Trigonometric Ratios (sin, cos and tan), the Sine Law or the Cosine Law. She also needs clarification on what each one (primary trig ratios, sine law, cosine law) can be used to calculate. Provide an explanation that will help to solidify her understanding. Be sure to discuss what each one will calculate and how to decide which one to use. Explanations, diagrams, examples, formulas and mathematical terminology should all be included in your solution. Be thorough!
    Here is a summary: you will need to think of examples and draw some diagrams.

    The Primary Trig Ratios will be used where you have a right-angled triangle. Draw a diagram showing a right-angled triangle, marking an angle of 90^o and labelling one of the other angles x. Label the three sides H, O and A, and write down the three ratios:

    \sin x = \frac{O}{H}, \cos x = \frac{A}{H} and \tan x = \frac{O}{A}

    Now explain (with a simple example of each) when you would use each of these formulae. For example, you'd use sine if you knew x and H, and wanted to calculate O; or you'd use tan if you knew O and A, and wanted to calculate x. The question asks you to be thorough, so make sure you include all three ratios in as many ways as you can think of.

    The Sine and Cosine Laws will be used where you have a non-right-angled triangle. Draw a diagram showing a triangle ABC, and write down the laws:

    Sine Law: \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

    And the three Cosine Laws: a^2 = b^2 +c^2 -2bc\cos A, b^2 = \dots, c^2 = \dots (I'll leave those to you)

    Then:

    Use the Sine Law if you know:

    • 2 angles and a side, and want a second side. (You may need to find the third angle first, using the fact that the three angles add up to 180^o.)
    • 2 sides and a non-included angle, and want a second angle. (This is called the Ambiguous Case because there may be two possible angles, one of which is the supplement of the second.)

    Use one of the Cosine Laws if you know:

    • 2 sides and the included angle, and want the third side.
    • 3 sides and want an angle.

    If you have 2 sides and the included angle, and want a second angle, you'll have to find the third side first, using the Cosine Law, and then the angle using the Sine Law.

    To be thorough in your answer, you could again think up some problems where you need to use these rules, and work out the answers showing how the formulae are used.

    I hope that gives you something to work on.

    Grandad
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