If cos b = 7 over 22, then which of the following is correct? a. csc b = 7 over 22 b. csc b = 22 over 7 c. sec b = 7 over 22 < this answer is wrong d. sec b = 22 over 7

The answer is Letter D - sec B = 22 over 7

For cosine = adjacent over hypotenuse; so the given are 7 as adjacent, and 22 as the hypotenuse. The opposite of cosine is secant, which can be computed as hypotenuse over adjacent. So:

sec B = 22 over 7

For this case we have the following expression:
  
 The first thing you should know for this case is the following trigonometric definition:
  
 Therefore, substituting the values we have:
  
 Rewriting the expression we have:
  
 
 the following is correct:
 d. sec B = 22 over 7