There are a few questions I have. They are about trigonometric functions and the quadrants that they are in. Can you explain how you got the answers? 1. If sint = 0.29 and sinw = 0.43, both t and w are positive, and the angles determined by t and w are in quadrant 2, then which of the following statements is true? a. t > w b. w > t c. Cannot be determined 2. If cost = - 0.42 and cosw = - 0.80, both t and w are positive, and the angles determined by t and w are in quadrant 3, then which of the following statement is true? a. t > w b. w > t c. Cannot be determined

Question 1:

sin (t) = 0.29

t = sin⁻¹ (0.29)

t = 16.86°

This value of sin (t) is in Quadrant 1, as shown below. All trigonometric function in quadrant 1 is positive. In quadrant 2, only Sine function is positive. In quadrant 2, sin (t) = 0.29 is given by the value of t = 180°-16.86° = 163.2°

sin (w) = 0.43

w = sin⁻¹ 0.43

w = 25.47°

In quadrant 2, sin (w) = 0.43 is given by the value of w = 180°-25.47° = 154.58°

163.2° > 154.53° = t > w

Question 2:

cos (t) = - 0.42

t = cos⁻¹ (-0.42)

t = 114.8

This value of t is in quadrant 2, where the value of Cosine is negative. In quadrant 3, the value of cos (t) = - 0.42 is given by t = 180°+65.2° = 245.2°

cos (w) = - 0.80

w = cos⁻¹ (-0.80)

w = 143.13

In quadrant 3, the value of cos (t) = - 0.80 is given by t = 180°+36.87° = 216.87°

245.2° > 216.87° = t > w