Question

Check all that apply, if csc theta=13/5, then:

A. sec theta= 5/13
B. tan theta= 5/12
C. sin theta= 5/13
D. cos theta= 5/13

Answer 1

csc θ = 13/5

`(1)/(sin. theta) =  (13)/(5)`

When you flip both sides:

sin θ = 5/13

If you know the Pythagorean triples, it will be 5, 12, and 13. Otherwise you could do a² + b² = c²

You can use:

`S(O)/(H) C(A)/(H) T(O)/(A)`

which is

`Sin (opposite)/(hypotenuse) Cos(adjacent)/(hypotenuse) Tan(opposite)/(adjacent)`

Or you could draw a triangle, either way works.

To find tangent, you know 13 is the hypotenuse because it is the longest side, and 5 is "opposite" so 12 is "adjacent. So:

tan theta = 5/12

And cosine is adjacent/ hypotenuse, so it is:

cos theta = 12/13

sec theta is the opposite of cos theta, so it is:

sec theta = 13/12

B and C are correct