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October 27th, 2016, 09:51 AM  #1 
Newbie Joined: Oct 2016 From: Rainfall Posts: 2 Thanks: 0  How to figure out the exact values?
I'm wondering how to solve problems like this: Sin^1(sin(90)) Can anyone help me with this? 
October 27th, 2016, 09:54 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,924 Thanks: 1521 
I assume the 90 is in degrees ... $\sin^{1}[\sin(90^\circ)] = \sin^{1}(1) = 90^\circ$ 
October 27th, 2016, 10:18 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra 
If $x=\sin^{1} \big( \sin 90^\circ \big)$ then $\sin x=\sin 90^\circ$

October 27th, 2016, 10:25 AM  #4 
Newbie Joined: Oct 2016 From: Rainfall Posts: 2 Thanks: 0 
What if it were sin^1(sin(180)) or cos^1(sin(330))?

October 27th, 2016, 11:39 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,924 Thanks: 1521 
I had a feeling this was going to be asked next ... $\sin^{1}[\sin(180^\circ)] = \sin^{1}(0) = 0$, because the range of the inverse sine function is $[90^\circ, 90^\circ]$ $\cos^{1}[\sin(330^\circ)] = \cos^{1}\left(\dfrac{1}{2}\right) = 120^\circ$ because the range of the inverse cosine function is $[0^\circ , 180^\circ]$ 

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