Question

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

Answer 1

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.
\[s^2+2^2=5^2\]
\[s^2=5^2-2^2\]
\[s=\sqrt{5^2-2^2}=\sqrt{25-4}=\sqrt{21}\]

Answer 2

yeah i got that

Answer 3

but how do I get the exact value?

Answer 4

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

Answer 5

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

Answer 6

wouldn't i have to multiply by square root of 21 to get rid of the square root?

Answer 7

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.

Answer 8

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?

Answer 9

take your time i will check back in a second.

Answer 10

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.

Answer 11

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

Answer 12

and what is the formula we use for that one?

Answer 13

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?

Answer 14

u there?