Let’s analyze the information provided to determine the relationship between [tex]\( t \)[/tex] and [tex]\( w \)[/tex].
1. We know that [tex]\(\sin t = 0.45\)[/tex] and [tex]\(\sin w = 0.89\)[/tex], and both angles [tex]\( t \)[/tex] and [tex]\( w \)[/tex] lie in the first quadrant.
2. In the first quadrant, the sine function is an increasing function. This means that as the angle increases from 0 to 90 degrees, the value of the sine function also increases from 0 to 1.
Given that [tex]\(\sin t = 0.45\)[/tex] and [tex]\(\sin w = 0.89\)[/tex]:
- Since [tex]\(\sin t = 0.45\)[/tex], [tex]\( t \)[/tex] is some angle such that its sine value is 0.45.
- Since [tex]\(\sin w = 0.89\)[/tex], [tex]\( w \)[/tex] is some angle such that its sine value is 0.89.
Because [tex]\( \sin \)[/tex] is an increasing function in the first quadrant, if [tex]\(\sin t < \sin w\)[/tex], then [tex]\( t < w \)[/tex].
Since 0.45 < 0.89, it follows that [tex]\( t < w \)[/tex].
Thus, the best statement that describes the relationship between [tex]\( t \)[/tex] and [tex]\( w \)[/tex] is:
A. [tex]\( w > t \)[/tex]
