given the function value and the quadrant restirction, find θ?

sin θ=-0.9744
 
(270°, 360°)

hello jo,
 
if you are given the value of the sine function, then the first step is to take the arcsine also known as sine inverse of that value, i.e.
 
θ = arcsin(-.9744) = -77.01º
 
however, you are asked to give this angle in the range (270º,360º). 
thus, you have to add 360º to that value (remember the sine and arcsine are periodic with period of 360º=2π).
 
therefore, θ = -77.01°+360º = 282.99º
 
note: be careful with how many decimal places you need to round! and a good sketch will show you why those two angles are equivalent geometrically.