## anonymous 4 years ago can someone explain how to find values of the six trigonometric functions when given: "Θ lies in Quadrant II. tan(Θ)=-24/7"

1. anonymous

2. anonymous

yeah, i'm not sure how to find it and i have four other problems for homework like it so i was wondering if someone could explain. do you knw?

3. anonymous

u want the value of $\Theta$??

4. anonymous

no i need to find the other six trigonometric functions by using the function of tan(Θ)

5. Mertsj

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6. Mertsj

$\sin \theta=\frac{side opposite}{hypotenuse}=\frac{24}{25}$

7. Mertsj

$\cos \theta=\frac{side adjacent}{hypotenuse}=\frac{-7}{25}$

8. anonymous

you just use that with all of the functions? i have them written down. (: but how did you get 25?

9. Mertsj

$\tan \theta=\frac{-24}{7}$

10. Mertsj

I got 25 by using the Pythagorean Theorem

11. Mertsj

now the other functions are the reciprocals of those already given:

12. Mertsj

$\cot \theta=\frac{1}{\tan \theta}=\frac{-7}{24}$

13. Mertsj

$\sec \theta=\frac{1}{\cos \theta}=\frac{-25}{7}$

14. Mertsj

$\csc \theta=\frac{1}{\sin \theta}=\frac{24}{25}$

15. anonymous

thank you ! i'm still a little confuzed about the 25. $a ^{2}+b ^{2}=c ^{2}$ ? right?

16. Mertsj

yes

17. anonymous

OH i'm sorry i get it now. i wasn't square rooting the final answer. thank you so much !

18. Mertsj

$7^2+24^2=c^2=49+576=625$

19. Mertsj

$c^2=625$

20. Mertsj

$c=\sqrt{625}=25$

21. anonymous

thank you!