trig help finding functions?

Question

How do you find tangent beta if sec beta is 3?

Answer 1

Step 1: Use sec b to find cos b.
sec b = 3
sec b = 1 / cos b
3 = 1 / cos b
cos b = 1/3

Step 2: Use cos^2 + sin^2 = 1 to find sin b:
cos^2 b + sin^2 b = 1
(1/3)^2 + sin^2 b = 1
1/9 + sin^2 b = 1
sin^2 b = 8/9
sin b = √8 / √9 = 2√2 / 3

Step 3: Now that you have sin b and cos b, you can find tan b:
tan b = sin b / cos b
tan b = (2√2 / 3) / (1/3)
tan b = 2√2 (solution!)

Answer 2

sec beta = 1/(cos beta)
so 1/(cos beta) =3,
rearranging that you get cos beta =1/3
then whack that into ur calculator to find the angle "beta" and then substitute ur answer for beta into tangent beta on ur calc. again and then you get the answer!!