Use the given info to find the exact value of (a) sin a/2, (b) cos a/2, and (c) tan a/2. tan a= -5/12, pi/2<a<pi

Question

(a) sin a/2=

(b) cos a/2=

(c) tan a/2=

Answer 1

Use the given info to find the exact value of (a) sin a/2, (b) cos a/2, and (c) tan a/2. tan a= -5/12, π/2<a<π

π/2 < a < π <== Angle a is in 2nd Quadrant

tan a = -5/12 Therefore cos a = -12/13

(1/2)(π/2 < a < π) ==> π/4 < a/2 < π/2 <== Angle a/2 is in 1st Quadrant, therefore:

(a) sin a/2 = √(1 - cos a)/2 = √(1 - (-12/13))/2 = √(1 + 12/13)/2 = √(13 + 12)/13/2 = √25/26 = (5√26)/26

(b) cos a/2 = √(1 + cos a)/2 = √(1 + (-12/13))/2 = √(1 - 12/13)/2 = √(13 - 12)/13/2 = √1/26 = √26)/26

(c) tan a/2 = (sin a/2)/(cos a/2) = (5√26)/26)/(√26)/26) = 5