Trigonometric Functions Problem

If theta is a fourth-quadrant angle such that sec theta= 4, use a trigonometric identity to find the exact value of tan theta. Decimal answers are not allowed. Use simplified radical form, if necessary.

I don't know about trig identities, I'd just do it with a triangle.
Draw a right angled triangle
label one of the acute angles theta,
Put 4 on the hypotenuse and 1 on the adjacent side. Now you have sec theta = 4
use pythagoras to get the other side as square root 15.
tan theta = opp/adj=root15/1 but it is in the 4th quad so it is negative
tan theta = -root15

You sound hot

thanks.

1+(tan theta)^2 = (sec theta)^2
tan theta = 4^2 - 1= 15
tan theta = 15^0.5 or -(15^0.5)
Because it's in the fourth quadrant, so tan theta must be negative
So tan theta = -(15^0.5)

Thanks MrBigbig.
I don't know why I didn't think of that.