Determine the exact values of sin x/2 cos x/2 tan x/2 using the half angle formulas if tan x= 4/3, pi < x < 3pi/2

Question

Determine the exact values of sin x/2 cos x/2 tan x/2 using the half angle formulas if tan x= 4/3, pi < x < 3pi/2

Answer 1

From the given fact, we know that cos x = -3/5 and sin x = -4/5.  (Mr. Pythagoras helps in this.)

 

Now you can use the half angle formula for sin ½x = √[(½(1-cos x)] and cos ½x = -√([½(1-+cos x)].

 

The latter formula has a negative sign preceding the radical because the half angle will be in quadrant II, where cosines are all negative.

 

Finally, the tan ½x = sin ½x / cos½x .