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

1. 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. $s^2+2^2=5^2$ $s^2=5^2-2^2$ $s=\sqrt{5^2-2^2}=\sqrt{25-4}=\sqrt{21}$

2. anonymous

yeah i got that

3. anonymous

but how do I get the exact value?

4. anonymous

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

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

6. anonymous

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

7. 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.

8. 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?

9. anonymous

take your time i will check back in a second.

10. 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.

11. anonymous

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

12. anonymous

and what is the formula we use for that one?

13. 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?

14. anonymous

u there?