if sec theta=-5/4 and 180degree < theta< 270degree, find tan theta
a.-3/5
b 4/5
c.3/4
d.3/5
secθ=-5/4; and θ is in the third quadrant, then
cosθ=1/secθ=-4/5
sinθ=sqrt(1-(-4/5)^2)=-3/5 (third quadrant)
So
tanθ
=sinθ / cosθ
= ?
To find the value of tan(theta), we need to use the relationship between tangent and secant:
tan(theta) = 1 / sec(theta)
Given that sec(theta) = -5/4, we substitute it into the equation:
tan(theta) = 1 / (-5/4)
To divide by a fraction, we multiply by its reciprocal:
tan(theta) = 1 * (4/-5)
Simplifying the expression:
tan(theta) = -4/5
Therefore, the answer is option a) -4/5.