# Thread: Where do I start this triq problem?

1. ## Where do I start this triq problem?

I need to find the 5 triq. expressions of $\displaystyle csc=-4$ I know the properties, but I'm not sure which expression I need to start with to find the other 4 expressions.$\displaystyle csc=\frac{1} {sin}$ is sin the receprical of-4, so it will be $\displaystyle sin= \frac{1}{4}$?

Thanks
Jason

2. Originally Posted by Darkhrse99
I need to find the 5 triq. expressions of $\displaystyle csc=-4$ I know the properties, but I'm not sure which expression I need to start with to find the other 4 expressions.$\displaystyle csc=\frac{1} {sin}$ is sin the receprical of-4, so it will be $\displaystyle sin= \frac{1}{4}$?

Thanks
Jason
I ignored this in your last thread, but i must say something now. you cannot have trig functions standing alone. writing csc and sin makes no sense! write csc(x) and sin(x) or whatever variable you want, they must be operating on something. that being said, you are right. csc(x) = 1/sin(x)

so if csc(x) = -4, then sin(x) = -1/4

now continue with the others

3. Sorry about that. I'll make sure to write it as Tan (x) as that is the variable we are using.

4. Does $\displaystyle Cos(x) = \frac{\sqrt17} {4}$ and $\displaystyle tan (x) =\frac{1} {\sqrt17}$?

5. Originally Posted by Darkhrse99
Does $\displaystyle Cos(x) = \frac{\sqrt17} {4}$ and $\displaystyle tan (x) =\frac{1} {\sqrt17}$?
Nope. where did 17 come from?

6. Sin (x)was $\displaystyle \frac{1} {4}$ so $\displaystyle 1^2+ 4^2=17, x={\sqrt17}$? Adjacent =$\displaystyle {\sqrt17}$

7. Originally Posted by Darkhrse99
Sin (x)was $\displaystyle \frac{1} {4}$ so $\displaystyle 1^2+ 4^2=17, x={\sqrt17}$?
no. 4 is the length of the hypotenuse. remember, sine = opposite/hypotenuse. thus you want 4^2 - 1^2.

alternatively, you can use the famous trig identity: $\displaystyle \sin^2 x + \cos^2 x = 1$

8. so it is $\displaystyle cos (x)=\frac{\sqrt15} {4}$and $\displaystyle tan (x)= \frac{1}{\sqrt15}$?

9. Originally Posted by Darkhrse99
so it is $\displaystyle cos (x)=\frac{\sqrt15} {4}$and $\displaystyle tan (x)= \frac{1}{\sqrt15}$?
we need to know what quadrant we are in to know what the sign of the cosine (and hence the tangent) is

10. CSC (t) is in the 4th quad, so $\displaystyle cos(x)=\frac{\sqrt15} {4} and Tan (x)=\frac{-1} {\sqrt15}$

11. Originally Posted by Darkhrse99
CSC (t) is in the 4th quad, so $\displaystyle cos(x)=\frac{\sqrt15} {4} and Tan (x)=\frac{-1} {\sqrt15}$
correct

now you can find the others

12. Thanks, I should have cought that So the answer is now right, right?

13. Originally Posted by Darkhrse99
Thanks, I should have cought that So the answer is now right, right?
yeah