Question

Given that tan(t) =
5 12, and 0 < t < π 2, complete the steps to find cos(t).

Which identity would be best to start with?

Answer 1

tan2(t)+1=sec2(t)  this is completely correct                                     

Answer 2

Answer:

cos (t) = $\frac {13} {12}$

tan(t) = $\frac {5} {12} = \frac {Opposite \quad side} {Adjacent \quad side}$

cos(t) = $\frac {Hypothesis} {Adjacent \quad side}$

Opposite side = 5, Adjacent side = 12

According to the Pythagoras Theorem,

$(Hypothesis)^2 = (Opposite \quad side)^2 + (Adjacent \quad side)^2$

              $= 5^2 + 12^2 = 25 + 144 = 169$

Hypothesis = $\sqrt {169}$

             = 13

cos(t) = $\frac {Hypothesis} {Adjacent \quad side} = \frac {13} {12}$