Question 979151
Since tangent is negative and secant is positive, this forces the angle to be in quadrant 4.


Draw a right triangle in this quadrant. Make the opposite leg (from the angle) 9 units long. Make the adjacent leg 5 units long. Use the pythagorean theorem to solve {{{5^2+9^2 = c^2}}} to get {{{c = sqrt(106)}}}


So the sine of that angle is {{{opposite/hypotenuse = -9/(sqrt(106))}}}


Notes: 


1) You can rationalize the denominator, but some books allow you to have that result. If you have to rationalize the denominator, then you should get {{{(-9*sqrt(106))/106}}}


2) Sine is negative in Q4.