if sec theta = square root 13 over 2, find tan theta of the given angle

Question

pls hurry i have a test

 

Answer 1

sec = hyp/adj

a² + b² = c²

2² + a² = (√13)²

4 + a² = 13

a² = 9

a = 3

tan θ = opp/adj

tan θ = 3/2

 

 

 

Answer 2

One of the fastest ways to find thus one is using the identity:

Tan²Θ + 1 = Sec²Θ

Simply plug in the value of the secant you were given, then solve for Tangent. Don't forget that your answer could be positive or negative, since you weren't given enough information to tell if this is happening in quadrant I or IV.