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anonymous

  • 5 years ago

if cos0 <0 and sin0= 2/5, find the exact value of tan0

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  1. anonymous
    • 5 years ago
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    easiest way to do this is draw a triangle. think of sine as opposite over hypotenuse, so label the opposite side 2 and the hypotenuse 5. all you need is the other leg which you get by pythagoras. \[s^2+2^2=5^2\] \[s^2=5^2-2^2\] \[s=\sqrt{5^2-2^2}=\sqrt{25-4}=\sqrt{21}\]

  2. anonymous
    • 5 years ago
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    yeah i got that

  3. anonymous
    • 5 years ago
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    but how do I get the exact value?

  4. anonymous
    • 5 years ago
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    tan is opposite of adjacent, so you you get \[tan(\theta)=-\frac{5}{\sqrt{21}}\] negative because you are told cosine is negative.

  5. anonymous
    • 5 years ago
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    that is the 'exact value' if you want a decimal approximation you have to use a calculator, but that is not "exact".

  6. anonymous
    • 5 years ago
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    wouldn't i have to multiply by square root of 21 to get rid of the square root?

  7. anonymous
    • 5 years ago
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    if you want to rationalize the denominator that is fine, but rather unnecessary unless you have a math teacher that insists that you do it. you just get \[-\frac{5 \sqrt{21}}{21}\] which doesn't look that much better. in fact it looks worse.

  8. anonymous
    • 5 years ago
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    yes he does insist on it! I wish he didn't. I got everything im just checking all my answers if you don't mind?

  9. anonymous
    • 5 years ago
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    take your time i will check back in a second.

  10. anonymous
    • 5 years ago
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    heres a question im not sure about. Find the length of an arc cut off by a central angle of 1.5 radians in a circle of radius 6 inches.

  11. anonymous
    • 5 years ago
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    radian measure is arc length divided by radius. so if we call the arc length a you have \[\frac{a}{6}=1.5\] \[a=6\times 1.5 = 9\]

  12. anonymous
    • 5 years ago
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    and what is the formula we use for that one?

  13. anonymous
    • 5 years ago
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    and, from a point on the ground, 238 ft from the foot of a vertical tower, the angle of elevation of the top of the tower is 43 degrees. what is the height of the tower to the nearest tenth?

  14. anonymous
    • 5 years ago
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    u there?

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