Question

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

a. - sqrt(5/26)
b. sqrt(5/26)
c. - sqrt(1/26)
d. sqrt(1/26)

Answer 1

Hence, the value of:

`\sin (x)/(2)=\sqrt(1)/(26)`

Explanation:

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

`\sin x=(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=(CB)/(AB)\\\\\cos x=(12)/(13)`

Now, we know that:

`\cos x=1-2\sin^2 (x)/(2)\\\\2\sin^2 (x)/(2)=1-\cos x\\\\sin^2 (x)/(2)=(1-\cos x)/(2)\\\\\sin^2 (x)/(2)=(1-(12)/(13))/(2)\\\\\sin^2 (x)/(2)=(13-12)/(2* 13)\\\\\\\sin^2 (x)/(2)=(1)/(26)\\\\\sin (x)/(2)=\sqrt{(1)/(26)}`

Answer 2

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).