October 9, 2015

Homework Help: inverse trig function

Posted by Jen on Monday, April 9, 2007 at 2:08pm.

How do I do this by sketching a triangle.
sin( arcsin(1/2) + arccos(1/2) )

let's start with arcsin(1/2)

draw a right angled triangle where theta and alpha are the two angles other than the 90 angle.
suppose you make the opposite side 1, and the hypotenuse 2.
Now look at the other angle alpha. Wouldn't the cosine of that angle also be 1/2??
(if you know your 30, 60, 90 triangle ratios, you will realize that the two angles are 30 and 60)

but since theta + alpha must total 90, you are really just being asked for sin 90, which is 1
so the answer is 1

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