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

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0easiest 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. \[s^2+2^2=5^2\] \[s^2=5^22^2\] \[s=\sqrt{5^22^2}=\sqrt{254}=\sqrt{21}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but how do I get the exact value?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0tan is opposite of adjacent, so you you get \[tan(\theta)=\frac{5}{\sqrt{21}}\] negative because you are told cosine is negative.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that is the 'exact value' if you want a decimal approximation you have to use a calculator, but that is not "exact".

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wouldn't i have to multiply by square root of 21 to get rid of the square root?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if 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
 5 years ago
Best ResponseYou've already chosen the best response.0yes 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
 5 years ago
Best ResponseYou've already chosen the best response.0take your time i will check back in a second.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0heres 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
 5 years ago
Best ResponseYou've already chosen the best response.0radian 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
 5 years ago
Best ResponseYou've already chosen the best response.0and what is the formula we use for that one?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and, 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?
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