## arindameducationusc one year ago Without calculator,steps for finding cos inverse(8/208)?

1. amilapsn

$\arccos{\frac{8}{208}}=\arccos{\frac{1}{26}}=\frac{\pi}{2}-\arcsin{\frac{1}{26}}\approx \frac{\pi}{2}-\frac{1}{26}$because for small $$\theta$$, $$\sin\theta=\theta\Rightarrow\arcsin\theta=\theta$$

2. arindameducationusc

3. arindameducationusc

please do all in steps.... Till I get 88 degrees

4. ganeshie8

Nice! @arindameducationusc are you saying you don't know how to convert $$\frac{\pi}{2}-\frac{1}{26}$$ from radians to degrees ?

5. amilapsn

$\arccos{\frac{8}{208}}\approx\frac{\pi}{2}-\frac{1}{26}=\left(\left(\frac{\pi}{2}-\frac{1}{26}\right)\times \frac{180}{\pi}\right)^o\approx88^o$

6. amilapsn

Are you ok @arindameducationusc ?

7. arindameducationusc

It should be (pi/2-1/26)*pi/180.... @amilapsn @ganeshie8

8. arindameducationusc

No, I got it....my bad..... silly mistakes do happen! LOL...!!!! I got it@amilapsn

9. ganeshie8

whichever you're converting to, that must be on top : radians to degrees : 180/pi degrees to radians : pi/180

10. arindameducationusc

Thank you. one question @ganeshie8 why did we use pi/2-arcsin(theota)?????

11. arindameducationusc

12. ganeshie8

familiar with this identity $$\arcsin(x)+\arccos(x)=\frac{\pi}{2}$$ ?

13. arindameducationusc

o yes, got it...! thank you.....

14. ganeshie8

np :) you also need to know the small angle approximation of $$\sin\theta$$ when $$\theta$$ is small, we can replace $$\sin\theta$$ by $$\theta$$