## anonymous 5 years ago find cos(sin-1(3/5))

1. anonymous

Draw a right angled triangle.

2. anonymous

done

3. anonymous

can't you just plug it in your calculator? find the inside function and then put that value into the cos equation?

4. anonymous

no calculator allowed

5. anonymous

Yes, you can put it in you calculator... and learn nothing.

6. anonymous

OK so a triangle has an angle (x) - if sin of this angle is 3/5, then one side of the triangle is 3, and the other 5 (by definition). Use pythagoras to work out the other side, and then cos (by definition).

7. anonymous

x = sin^-1(3/5), by the way

8. amistre64

sin(a) = 3/5 sin^2 + cos^2 = 1 (3/5)^2 + cos^2 = 1 cos^2 = 1 - 9/25 cos^2 = 16/25 cos(a) = 4/5

9. amistre64

cos-1(cos(a)) = 4/5

10. anonymous

cos^-1(cos(a)) = a, actually ;)

11. amistre64

hmm..... thats right. lol

12. amistre64

there aint no simple angles from trig to give you a cosine of 4/5; or a sin of 3/5 :)

13. anonymous

14. anonymous

Yes (but my method was better :p)

15. anonymous

what would cos(sin(3/5)) be?

16. anonymous

That would be .. a lot harder (if neither are ^-1)

17. anonymous

sorry cos-1(sin(3/5))

18. anonymous

woops

19. anonymous

$\cos^{-1}\left[\sin\left(\frac{3}{5}\right)\right] = x \iff \sin\left(\frac{3}{5}\right) = \cos(x)$

20. anonymous

Are you working in radians or degrees?

21. anonymous

radians i assume. the problem calls for the exact value

22. anonymous

By definition: $\sin(\alpha) = \cos\left(\frac{\pi}{2}-\alpha\right) \text{ and } \cos(\alpha) = \sin\left(\frac{\pi}{2}-\alpha\right)$

23. anonymous

So if sin(3/5) = cos(x), then x = ....

24. anonymous

3/5 ?

25. anonymous

im sorry those formulas are in my book and i can't understand them.

26. anonymous

They aren't in your book, do you mean?

27. anonymous

are. i have example problems i just wanted it broken down.

28. anonymous

i have to go. thanks for the bit of help though! sorry i couldn't do more with it

29. anonymous

Oh, OK. Well, they work because cos is just a translation of sin, by pi/2. The answer is x = pi/2 - 3/5, from the formulae