## allisonhe 2 years ago Determine the values of sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ at (-3, -4) on the terminal arm of an angle θ in standard position.

1. aussy123

hi, ill show you by doing it in a^2+b^2=c^2

2. aussy123

|dw:1366290386156:dw|

3. aussy123

Ok in order to figure out sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ, you must know its properties.

4. aussy123

In quad 1 all of the properties are positive In quad 2 on sin and csc are positive In quad 3 only tan and cot are positive In quad 4 only cos and sec are positive

5. aussy123

For your we are in quad 3, so only tan and cot are positive.

6. aussy123

7. aussy123

so tan θ= 3/4 Its positive because tan θ is positive in 3rd quad. and since we know tanθ, we know cotθ. cotθ is the reciprocal of tanθ, being that it is adjacent over opposite. so cot θ = 4/3. Remember dont mark negative just because it is given that way. Follow the rules of the quads.

8. aussy123

Now we use a^2 +b^2=c^2 formula to solve

9. aussy123

|dw:1366291285028:dw|

10. aussy123

|dw:1366291332244:dw|

11. aussy123

|dw:1366291457845:dw|

12. aussy123

Now Using what is above you can solve for the rest by following these rules. sinθ= Opposite over Hypotenuse ONLY POSITIVE IN QUAD 1 and QUAD 2 cscθ=Hypotenuse over Opposite __________________________________________________ cosθ= Adjacent over Hypotenuse ONLY POSITIVE IN QUAD 1 AND 4 secθ= Hypotenuse over Adjacent HOPE YOU FOUND THIS HELPFUL! :)

13. aussy123

Did you find the rest?

14. allisonhe

yes, and i think this helpful

15. aussy123

Ok Happy to know! Have a great Day!