Question 29 Use the information given about the angle theta

Question #29

Use the information given about the angle theta, 0 lessthanorequalto theta lessthanorequalto 2 pi, to find the exact value of the indicated trigonometric function. sin theta 1/4, 0

Solution

29) sin = 1/4

cos =  (15/16) = 2*cos² (/2) - 1 ========> cos(/2) = ((15)/8 + 1/2)

Now sin = 2*sin/2*cos(/2) ========> sin/2 = sin/(2*cos(/2))

  sin/2 = (1/4)/(2*((15)/8 + 1/2)) = 1/(8*((15)/8 + 1/2)) = 1/(4*((15)/2 + 2))

30) sin = 1/4, tan > 0 [1st quadrant]

cos =  (15/16) = 2*cos² (/2) - 1 ========> cos(/2) = ((15)/8 + 1/2) = [(2(15) + 8)]/4 (option D)