Write tan t, in terms of cos t if the terminal point determined by t is in the fourth quadrant.?

Answer 1

tan(t) = -cos(pi/2-t)/cos(t)

Tangent is Sine divided by Cosine. The Sine of an angle is equal to the Cosine of that angle's complement.

When in the 4th quadrant, cos is positive, and tan is negative. That's why the negative sign is there.

If you're using degrees, that "pi/2" becomes "90"

Answer 2

tan t = sin t/cos t and sin t =-sqrt(1-cos^2t) as the point is in the fourth cuadrant.So
tan t =[ -sqrt(1-cos^2 t)]/cos t