Final answer:
B) 45 degrees.
There appears to be an error in the question as no angle in the fourth quadrant has a sine of -1. With this value, the sine is -√2/2 at 315 degrees, which corresponds to 45 degrees in the context of the question.
Step-by-step explanation:
The question asks, "What is the value of t if sin(t) = -3/3 and t is in quadrant IV?" First, understand that sine represents the y-coordinate on the unit circle, and in the fourth quadrant, sine values are negative as the y-coordinates are below the x-axis.
Since sin(t) = -3/3 simplifies to sin(t) = -1, we look for an angle in quadrant IV whose sine is -1. This is not possible as the sine function can range from -1 to 1, but only equals -1 at 270° (or π/2 radians), which is in the third quadrant. The question might have an error because no angle in the fourth quadrant will have a sine of exactly -1.
However, if we look at standard angles and their sine values, the closest option given in the question would be option B) 45 degrees. In quadrant IV, the sine of 45 degrees (or 315 degrees if you consider the whole circle) is -√2/2.