Question

If sinx = 5/13 and x is in quadrant 1, then sin x /2 = .....

Answer 1

Sinx=5/13 then cosx=12/13 sin(x/2) =sqrt(1-cosx/2) =sqrt(1-12/13)/2 =sqrt(1/26) =1/sqrt(26) 
So, the answer will be D option sqrt (1/26).

Answer 2

Answer:

Hence, the value of:

$\sin \dfrac{x}{2}=\sqrt\dfrac{1}{26}$

Step-by-step explanation:

We are given a trignometric formula for the given angle 'x' as:

$\sin x=\dfrac{5}{13}$

So, we consider a right  triangle such that it's perpendicular side is 5 units and the hypotenuse is 13 units.

Hence, we get the third side of the triangle i.e. CB using the Pythagorean Theorem as:

$AB^2=CB^2+AC^2\\\\13^2=CB^2+5^2\\\\169=CB^2+25\\\\CB^2=169-25\\\\CB^2=144\\\\CB=12\ units$

Hence,

$\cos x=\dfrac{CB}{AB}\\\\\cos x=\dfrac{12}{13}$

Now, we know that:

$\cos x=1-2\sin^2 \dfrac{x}{2}\\\\2\sin^2 \dfrac{x}{2}=1-\cos x\\\\sin^2 \dfrac{x}{2}=\dfrac{1-\cos x}{2}\\\\\sin^2 \dfrac{x}{2}=\dfrac{1-\dfrac{12}{13}}{2}\\\\\sin^2 \dfrac{x}{2}=\dfrac{13-12}{2\times 13}\\\\\\\sin^2 \dfrac{x}{2}=\dfrac{1}{26}\\\\\sin \dfrac{x}{2}=\sqrt{\dfrac{1}{26}}$