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Math Help - Find the exact values

  1. #1
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    Find the exact values

    For each pair of values of sin(`theta) and cos(`theta), find the exact values of the four remaining trigonometric functions, when this is possible; otherwise find the four remianing functions to 3 significant figures:

    sin(`theta)= 3/5, cos(`theta)= -4/5

    sin(`theta)= .9170001, cos(`theta)= 3.98
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  2. #2
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    Apply Pythagorean Theorem and find the missing value..

    x^2 + y^2 = r^2

    Where x being the adjacent side, y being the opposite side, and r is the hypotenuse.

    Now that you got the values of x, y, and r, simply replace it in the 6 trigonometric ratios.

    \sin{\theta} = \frac{y}{r}

    \cos{\theta} = \frac{x}{r}

    \tan{\theta} = \frac{y}{x}

    \csc{\theta} = \frac{r}{y}

    \sec{\theta} = \frac{r}{x}

    \cot{\theta} = \frac{x}{y}
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  3. #3
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    I got the first part but to be able to do the last part's of the question I would need more than one number. Should I put them over 1 or what? I am confused about what to do with sin(`theta)= .9170001, cos(`theta)= .398 since they are in decimal form.
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  4. #4
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    Then convert them to fractions and reduce the fraction to it's lowest terms. You do know how to convert a decimal to a fraction, right?
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  5. #5
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    Yes. I see now. Thanks!
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  6. #6
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    Quote Originally Posted by christenc05 View Post
    For each pair of values of sin(`theta) and cos(`theta), find the exact values of the four remaining trigonometric functions, when this is possible; otherwise find the four remianing functions to 3 significant figures:

    sin(`theta)= 3/5, cos(`theta)= -4/5

    sin(`theta)= .9170001, cos(`theta)= 3.98
    Let us do them in another way.

    sin(`theta)= 3/5, cos(`theta)= -4/5

    That means for angle theta,
    opposite sde ...(opp)... = 3
    hypotenuse.....(hyp)... = 5
    adjacent side ..(adj)... = -4

    So,
    tan(theta) = opp/adj = 3/(-4) = -3/4
    cot(theta) = adj/opp = (-4)/3 = -4/3
    sec(theta) = hyp/adj = 5/(-4) = -5/4
    csc(theta) = hyp/opp = 5/3

    --------------------------------
    sin(`theta)= .9170001, cos(`theta)= 3.98

    That means for angle theta,
    opposite sde ...(opp)... = 0.9170001
    hypotenuse.....(hyp)... = 1
    adjacent side ..(adj)... = 3.98

    So,
    tan(theta) = opp/adj = 0.9170001 /3.98 = 0.2304
    cot(theta) = adj/opp = 3.98 /0.9170001 = 4.34024
    sec(theta) = hyp/adj = 1 /3.98 = 0.25126
    csc(theta) = hyp/opp = 1 /0.9170001 = 1.09051
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