Question

If sin ? = 12 over 37, use the pythagorean identity to find cos ?. cos ? = ± 35 over 37 cos ? = ± 23 over 37 cos ? = ± 35 over 12 cos ? = ± 20 over 35

Answer 1

SOH CAH TOA
Lets us know that the Sin of ? Is 12/37; meaning the opposite side is 12, and the hypotenuse is 37. Using the Pythagorean Theorem, we know that 37^2-12^2=B^2 (B being the adjacent side). Once solved, we learn B is 35. Going back to SOH CAH TOA, we know that Cos ?= 35/37; the first option.

Hope this helps!

Answer 2

If sin x = 12/37, we have to find cos x.
The identity:
sin² x + cos² x = 1
( 12/37)² + cos² x = 1
144 / 1369 + cos² x = 1
cos² x = 1 - 144/1369
cos² x = 1369/1369 - 144/1369
cos² x = 1225 / 1369
cos x = +/- √ 1225/1369 = +/- 35/37
Answer:
A ) cos ? = +/- 35 over 37