What is sec(10/9).................. PLEASE HELP!

If sec theta= 10/9 FIND:

csc theta=__________

sin theta=___________

cos theta=___________

tan theta=___________

cot theta=___________

*****NO DECIMALS******

For starters, there's a big different between Sec(10/9) and Sec(theta)= 10/9
The first one means that 10/9 is an angle.
The second means that the Sec calculation OF the angle theta = 10/9.

Anywhoo...

If sec(theta) = 10/9

Then simply use your identities:

Cos(x) = 1/Sec(x)
Sin(x) = 1/Csc(x)
Tan(x) = 1/Cot(x)

So if:

Sec(x) = 10/9

then:

Cos(x) = 9/10

Now we need to get it in terms of Sin(x) to finish the rest of the problems.

Recall the identity: Cos^2(x) + Sin^2(x) = 1

so that means:

Sin(x) = Sqrt(1-Cos^2(x))

Plug in our value for Cos(x):

Sin(x) = Sqrt(1-[(9/10)^2])

invert to find Csc(x):

1/{Sqrt(1-[(9/10)^2])}

and Tan(x) = Sin/Cos so:

(10/9)*Sqrt(1-[(9/10)^2])

and inverting Tan(x) gives us Cot(x):

9/{10*Sqrt(1-[(9/10)^2])}