anonymous
  • anonymous
if cos0 <0 and sin0= 2/5, find the exact value of tan0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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. \[s^2+2^2=5^2\] \[s^2=5^2-2^2\] \[s=\sqrt{5^2-2^2}=\sqrt{25-4}=\sqrt{21}\]
anonymous
  • anonymous
yeah i got that
anonymous
  • anonymous
but how do I get the exact value?

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anonymous
  • anonymous
tan is opposite of adjacent, so you you get \[tan(\theta)=-\frac{5}{\sqrt{21}}\] negative because you are told cosine is negative.
anonymous
  • anonymous
that is the 'exact value' if you want a decimal approximation you have to use a calculator, but that is not "exact".
anonymous
  • anonymous
wouldn't i have to multiply by square root of 21 to get rid of the square root?
anonymous
  • anonymous
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.
anonymous
  • anonymous
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?
anonymous
  • anonymous
take your time i will check back in a second.
anonymous
  • anonymous
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.
anonymous
  • anonymous
radian measure is arc length divided by radius. so if we call the arc length a you have \[\frac{a}{6}=1.5\] \[a=6\times 1.5 = 9\]
anonymous
  • anonymous
and what is the formula we use for that one?
anonymous
  • anonymous
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?
anonymous
  • anonymous
u there?

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