Show all your work and place your answers in the boxes If se

Show all your work and place your answers in the boxes. If sec theta = -5 and sin theta > 0, find the EXACT values of the following: cot(pi/2 - theta) sin(theta + pi) Find all solutions of the equation 3 sin^2 x + 7 = 13 cos x in the interval [0 degree, 360 degree).

Solution

cot (pi/2 - theta) = tan theta

tan = y / x
sec = r / x = -5 (since sin t > 0) = 5 / -1
thus, x = -1 and r = 5

x^2 + y^2 = r^2

y^2 = 24

y = sqrt(24)

y= 2sqrt(6)

cot (pi/2 - theta) = tan theta

= y / x

= 2sqrt(6) / -1

= -2sqrt(6)
sin (theta + pi) = - sin theta

= - y / r

= -2sqrt(6) / 5
sin (theta+ pi) = -2sqrt(6) / 5