Question

Assume sin t = .45 and sin w = .89, both t and w are positive, and both t and w determine a terminal point in quadrant 1. Which of the following statements best describes the relationship between t and w?

A. t>w
B. w>t
C. It is not possible to tell from the given information.

Please explain answer. Thank you!

Answer 1

First quadrant implies the angle with the x-axis is between 0 and 90 degrees.
In the first quadrant, the sine function INCREASES from 0 to 1 (sin(0) = 0, sin(90) = 1).
Since sin(w) > sin(t),
w > t in the first quadrant.

Answer 2

We may plot a diagram first.
Both t and w terminate in the first quadrant.