If cosx=-1/2 x lies in the 3rd quadrant Find sinx/2,cosx/2,tanx/2 - Maths - Trigonometric Functions

Question

If cosx=-1/2 x lies in the 3rd quadrant Find sinx/2,cosx/2,tanx/2

Manbar Singh · Accepted Answer

We have,cos x = -12Since, π≤x≤3π2 ⇒ π2≤x2≤3π4Now, when θ lies in second quadrant, then cos θ is negative, sin θ is positive
Now, cosx2 = -1+cos x2 = -1+-122 = -14 =-12sinx2 = 1-cos x2 = 1--122 = 32tanx2 = sinx/2cosx/2 = 3/2-1/2 = -3

If cosx=-1/2 x lies in the 3rd quadrant. Find sinx/2,cosx/2,tanx/2.