Question

Write the correct answer in the blank. 1. Which trigonometric function is positive in the third quadrant? 2. Which trigonometric function is positive in the fourth quadrant? 3. Which trigonometric function is positive in the second quadrant? Determine in which quadrant e would lie given the following information. 4. tan 0 > 0 and sin 0 < 0 5. cos 0<0 and sin e <0 6. sin 0 > 0 and cos 0 > 0 Answer the following questions using the given information. Show your work. cos 0= - , tan 0<0 mnd 7. In what quadrant does e lie? 8. sin 9. tan e COMPLETION the statet Solve each equation for 0 (0°e < 360°) 10. 2 sin 0= 1

Answer 1

1. In the 3rd quadrant, tan(theta) is positive, as in the third quadrant, both x and y are negative, and thus, tan(theta) = Perpendicular/Base =  -y/-x = y/x which is positive. cot(theta) is also positive as cot(theta) = 1/tan(theta)

2. In the 4th quadrant, cos(theta) is positive, as in the 4th quadrant, x is positive and y is negative, and thus, cos(theta) = Base/Hypotenuse =  x/sqrt(x^2 + y^2) which is positive. sec(theta) is also positive as sec(theta) = 1/cot(theta)

3. In the 2nd quadrant, sin(theta) is positive, as in the 2nd quadrant, y is positive and x is negative, and thus, sin(theta) = Perpendicular/Hypotenuse = y/sqrt(x^2 + y^2) which is positive. cosec(theta) is also positive as cosec(theta) = 1/sin(theta)

4. tan(theta) is positive in 1st and 3rd quadrant, and sin(theta) is negative in 3rd and 4th quadrant.

Thus, theta lies in 3rd quadrant.

5. cos(theta) is negative in 2nd and 3rd quadrant, and sin(theta) is negative in 3rd and 4th quadrant.

Thus, theta lies in 3rd quadrant.

6. cos(theta) is positive in 1st and 4th quadrant, and sin(theta) is positive in 1st and 2nd quadrant.

Thus, theta lies in 1st quadrant.