Question

Assume sin t =.45 and sin w =.89 both t and w are postive and both t and w determne a terminal point in a quadrant 1. which of the following statements best describe the relationship between t and w
a w>t
b t>w
C not possible to tell

Answer 1

Answer:

Option a - w>t

Step-by-step explanation:

Given : $sin t =0.45$ and $sin w =0.89$ both t and w are positive and both t and w determine a terminal point in a quadrant 1.

To find : Which of the following statements best describe the relationship between t and w?

Solution :

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

So, sin(w)=0.89 > sin(t)=0.45

Since sin(w) > sin(t),

w > t in the first quadrant.

Therefore, Option a is correct .

Answer 2

The sine function is increasing in the first quadrant.
sin(0) = 0
sin(90) = 1

This means the larger angle will give a larger sine value.
sin(w) > sin(t) -----> w > t