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Math Help - Trig. ratios and trig expressions

  1. #1
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    Trig. ratios and trig expressions

    hi so i need help for these Two questions:

    1. a) To find trigonometric ratios for 240 degrees using a unit circle, a Reference angle of 6 degrees is used. what reference angle should you use to find the trigonometric ratios for 210 degrees?

    b) Use the unit circle to find exact values of the three primary trig. ratios for 210 and 240 degrees

    2. A fishing boat is 15km south of a lighthouse. A yacht is 15km west of the same lighthouse.

    a) Use trigonometry to find an exact expression for the distance between the two boats.

    b) Check your answer using another method.

    Any help would be appreciated
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  2. #2
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    Hello sblocker

    Welcome to Math Help Forum!
    Quote Originally Posted by sblocker View Post
    hi so i need help for these Two questions:

    1. a) To find trigonometric ratios for 240 degrees using a unit circle, a Reference angle of 6 degrees is used. what reference angle should you use to find the trigonometric ratios for 210 degrees?
    I think you mean 60^o, not 6^o. Look at the diagram (click to enlarge):
    Trig. ratios and trig expressions-untitled.jpg
    Can you see that you'll use the angle of 30^o to find the ratios for 210^o?

    b) Use the unit circle to find exact values of the three primary trig. ratios for 210 and 240 degrees
    Write down the sine, cosine and tangent of 30^o and 60^o. (You should know what these are.)

    Can you see from the diagram that to get the sine, cosine and tangent of 210^o and 240^o you'll simply change the sign of all these values from + to - ?


    2. A fishing boat is 15km south of a lighthouse. A yacht is 15km west of the same lighthouse.

    a) Use trigonometry to find an exact expression for the distance between the two boats.

    b) Check your answer using another method.

    Any help would be appreciated
    No time to answer this now. I'll do so later if no-one else answers in the meantime.

    Grandad
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  3. #3
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    Hello again sblocker
    Quote Originally Posted by sblocker View Post
    2. A fishing boat is 15km south of a lighthouse. A yacht is 15km west of the same lighthouse.

    a) Use trigonometry to find an exact expression for the distance between the two boats.

    b) Check your answer using another method.

    Any help would be appreciated
    Take a look at the diagram:
    Trig. ratios and trig expressions-untitled.jpg
    (a) The triangle is right-angled at L, and, since it is isosceles (LY = LF), \angle F = 45^o.

    So:
    \sin 45^o = \dfrac{LY}{FY}

    \Rightarrow FY=\dfrac{LY}{\sin 45^o}
    =15\div\dfrac{1}{\sqrt2}

    =15\sqrt2
    (b) Using Pythagoras' Theorem:
    FY^2 = 15^2+15^2
    =15^2\times2
    \Rightarrow FY = 15\sqrt2

    Grandad
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