Given the following:sec(theta)=15/9 and cot<0. Find the remaining trig functions

Answer 1

sec(theta) = 1/cos(theta) = 1/(adjacent/hypotenuse) = hypotenuse/adjacent

Therefore, hyp/adj =15/9

hyp = 15, adj =9

According to the Pythagorean Theorem, adj^2 + opposite^2 = hyp^2

9^2 + opposite^2 = 15^2

81 + opp^2 = 225

opp^2 = 144

Therefore opp = 12

Now that you have all 3 values for adj, opp, and hyp, you can calculate all the other ratios.

According to SOHCAHTOA,

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

csc = 1/sin

sec = 1/cos

cot = 1/tan