SOLUTION: Hello. I really do appreciate what you do here, and this is definately one quesion that i will ever bothr you with. Would you be able to simplify arccos(sin(5pi/4))

Click here to see ALL problems on Trigonometry-basics

Question 132370: Hello. I really do appreciate what you do here, and this is definately one quesion that i will ever bothr you with.
Would you be able to simplify
arccos(sin(5pi/4))

Found 2 solutions by scott8148, stanbon:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
the angle whose cosine is the sine of 5pi/4

5pi/4 is a 45� angle in quadrant III __ the sine and cosine are equal

so, arccos(sin(5pi/4))=5pi/4
__ the smallest angle to satisfy the conditions is 3pi/4 in quadrant II

some people might call this a "trick" question

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
arccos(sin(5pi/4))
--------------
You want the cosine of the angel whose sine is (5/4)pi.
sin[(5/4)pi) = -sin[(1/4)pi] = -(1/2)sqrt2
----------------
The cosine of[(-1/2)sqrt(2)] = 0.7602 radians
==============
Cheers,
Stan H.