The problem states,
If sec(theta) = 3 with theta in QIV find cos(theta), sin(theta) and tan(theta).
you should know that secant is the reciprocal of cosine , so the fact that
should be immediate.
since is in quad IV , you should also know that and are both negative values.
there are two ways to determine the values of sine and tangent ...
1) use of reference triangles
sketch a reference right triangle in quad IV ... since , then the adjacent side = 1 and the hypotenuse = 3
the size of the opposite side =
since the opposite side has a downward direction, its value is .
2) use of Pythagorean identities ...
and, of course, you have to determine the correct sign from the quadrant info.