Question

If Sin X = -1/2 and X lies in Quadrant IV, find the values of

(i) sinx/2

(ii) cosx/2

(iii) tanx/2

Answer 1

Given: sinx = \(-\frac{1}{2}\) and x lies in Quadrant IV.

To Find:

(i) sin\(\frac{x}{2}\)

(ii) cos\(\frac{x}{2}\)

(iii) tan\(\frac{x}{2}\)

Now, since sinx = \(-\frac{1}{2}\)

We know that cosx = \(\pm\sqrt{1-sin^2\text{x}}\) 

since cosx is positive in IV quadrant, hence cosx \(\frac{\sqrt{3}}{2}\)

(i) sin\(\frac{x}{2}\)

Formula used:

Since sinx is negetive in IV quadrant, hence sin\(\frac{x}{2}=-\frac{\sqrt{2-\sqrt{3}}}{2}\)

(ii) cos\(\frac{x}{2}\)

Formula used:

(iii) tan\(\frac{x}{2}\).

Formula used:

tanx = \(\frac{sinx}{cosx}\)