Question

find the value of sin22.5​

Answer 1

This is your answer which is the value of sin 22.5

Answer 2

Answer:

0.382

Step-by-step explanation:

As given in question we have to find the value of

$sin22.5^o$

According to the formula

    $cos2\theta\ =\ cos^2\theta\ -\ sin^2\theta$

$=>\ cos2\theta\ =\ 1\ -\ sin^2\theta\ -\ sin^2\theta$

$=>\ cos2\theta\ =\ 1\ -\ 2.sin^2\theta$

$=>\ sin^2\theta\ =\ \dfrac{1\ - \ cos2\theta}{2}$

$=>\ sin\theta\ =\ \sqrt{\dfrac{1\ - \ cos2\theta}{2}}$

Now, put $\theta\ =\ 22.5^o$

we will get,

    $sin22.5^o\ =\ \sqrt{\dfrac{1\ - \ cos2\times 22.5^o}{2}}$

$=>\ sin22.5^o\ =\ \sqrt{\dfrac{1\ - \ cos45^o}{2}}$

                        $=\ \sqrt{\dfrac{1\ -\ \dfrac{1}{\sqrt{2}}}{2}}$

                        $=\ \sqrt{\dfrac{\sqrt{2}-1}{2\sqrt{2}}}$

                        = 0.382

Hence, the value of sin22.5​° is 0.382.