Question

if sin theta is 1÷√5 then cos theta​

Answer 1

Answer:

i think answer is correct

Answer 2

ANSWER:

Given:

• sin ө = 1/√5

To Find:

• cos ө

Solution:

We are given that,

$\implies \sin\theta=\dfrac{1}{\sqrt5}- - - - (1)$

But, we need to find cos ө

We know that,

$\hookrightarrow\sin^2\phi+\cos^2\phi=1$

So,

$\implies\cos^2\phi=1-\sin^2\phi$

$\implies\cos\phi=\sqrt{1-\sin^2\phi\:}$

Now, we need to find the value of

$\implies\cos\theta$

So,

$\implies\cos\theta=\sqrt{1-\sin^2\theta\:}$

From (1)

$\implies\cos\theta=\sqrt{1-\left(\dfrac{1}{\sqrt5}\right)^2\:}$

$\implies\cos\theta=\sqrt{1-\dfrac{1}{5}\:}$

$\implies\cos\theta=\sqrt{\dfrac{5-1}{5}\:}$

$\implies\cos\theta=\sqrt{\dfrac{4}{5}\:}$

Hence,

$\implies\bf cos\theta=\dfrac{2}{\sqrt5}$

Therefore, the value of cos ө is 2/√5