20 pts! ? trig

if sec(a) = 3/2 and < a is in the quadrant i, what is the value of tan(x)?

a. 2sqrt5 /3

b. sqrt5 /3

c. sqrt5 /2

d. 3sqrt5 /2

give me a short or long explanation on how to solve this if you can .

The answer is c, sqrt5 /2. Sec is 1/cos or r/x. Tan is y/x. With that being said, You would use Pythagorean Theorem to find y. So y^2 + 2^2 = 3^2. Y^2 + 4 = 9. Y= sqrt 5, in which y/x is sqrt 5/ 2. Hope this makes sense!

128/3reason being 5 and 1/3 = 16/316/3 • 2/3 = 32/31 and 1/3 = 4/3 32/3 • 4/3 this will equal 128/3