Find the exact value of the indicated trigonometric function of θ.

Question

Find the exact value of the indicated trigonometric
function of θ.

sec θ =3/2 , θ in quadrant IV

 

Find tan θ.

Answer 1

Hi Hannah,

 

sec theta = 1/cos theta

sec theta = 3/2

cos theta = 2/3  

tan theta = opp / adj

we know one side and the hypotenuse from cos theta = 2/3 since cos theta = adj/hyp

hyp^2 = adj^2 + opp^2 

3^2 = 2^2 + opp^2

opp = sqrt(5)

tan theta = -sqrt(5) / 2  (Since theta is in quadrant IV.  tan theta is negative)