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