Question

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

Answer 1

what the answer?

Answer 2

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?

Answer 3

u want the value of \[\Theta\]??

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

\[\tan \theta=\frac{-24}{7}\]

Answer 9

I got 25 by using the Pythagorean Theorem

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

\[\csc \theta=\frac{1}{\sin \theta}=\frac{24}{25}\]

Answer 14

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

Answer 15

yes

Answer 16

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

Answer 17

\[7^2+24^2=c^2=49+576=625\]

Answer 18

\[c^2=625\]

Answer 19

\[c=\sqrt{625}=25\]

Answer 20

thank you!