DimaMazin Posted March 11, 2021 Share Posted March 11, 2021 (61/2 - 21/2)/4 = (2 - 31/2)1/2/2 I have taken sin * cos=1/4 then I have got sine=(2 - 31/2)1/2/2 or (2 + 31/2)1/2/2 Calculator has shown arcsin=15 degrees but sine 15 degrees=(61/2 - 21/2)/4 I don't understand how they are connected. Link to comment Share on other sites More sharing options...
Ghideon Posted March 11, 2021 Share Posted March 11, 2021 1 hour ago, DimaMazin said: (61/2 - 21/2)/4 = (2 - 31/2)1/2/2 Hope this helps: yes the equality holds; quick check using Wolfram alpha gives that is equal to reference: https://www.wolframalpha.com/input/?i=(6^0.5-2^0.5)%2F4 1 hour ago, DimaMazin said: sin * cos=1/4 Not sure what that means Link to comment Share on other sites More sharing options...
DimaMazin Posted March 12, 2021 Author Share Posted March 12, 2021 21 hours ago, Ghideon said: Hope this helps: yes the equality holds; quick check using Wolfram alpha gives that is equal to reference: https://www.wolframalpha.com/input/?i=(6^0.5-2^0.5)%2F4 Not sure what that means For example one circular sector of unit circle has area a/2, other circular sector has area Pi/4 - a/2 then a/2=sin(a)*cosin(a)/2 +(area of circular segment of angle 2a)/2 and Pi/4 - a/2 = sin(a)*cosin(a)/2+(area of circular segment of angle Pi - 2a)/2 Then area of the twq equal triangles is sin*cosin Link to comment Share on other sites More sharing options...
Bufofrog Posted March 12, 2021 Share Posted March 12, 2021 46 minutes ago, DimaMazin said: For example one circular sector of unit circle has area a/2, So the area in question is 1/2 of the circle? 48 minutes ago, DimaMazin said: other circular sector has area Pi/4 - a/2 So that would mean that Pi/4 is the total area 'a'. Since Pi r^2 = area of a circle, Pi r^2 = Pi/4 or r = 0.5. Is that correct? Or are these areas small circles in the larger circle? Link to comment Share on other sites More sharing options...
DimaMazin Posted March 12, 2021 Author Share Posted March 12, 2021 7 hours ago, Bufofrog said: So the area in question is 1/2 of the circle? So that would mean that Pi/4 is the total area 'a'. Since Pi r^2 = area of a circle, Pi r^2 = Pi/4 or r = 0.5. Is that correct? Or are these areas small circles in the larger circle? Unit circle has r=1. a is angle in radians. You have confused in your inattentiveness . (61/2 - 21/2)/4 = (2-31/2)1/2/2 21/2(31/2-1)/2=(2-31/2)1/2 (31/2-1)2/2=2-31/2 3-2*31/2+1=4-2*31/2 Link to comment Share on other sites More sharing options...
Bufofrog Posted March 13, 2021 Share Posted March 13, 2021 10 hours ago, DimaMazin said: For example one circular sector of unit circle has area a/2, other circular sector has area Pi/4 - a/2 What do you mean by a sector? The area of a quadrant of the unit circle is Pi/4 and the area of the unit circle is Pi. What are these 2 sectors and why the relationship between the 2? Link to comment Share on other sites More sharing options...
DimaMazin Posted March 13, 2021 Author Share Posted March 13, 2021 3 hours ago, Bufofrog said: What do you mean by a sector? The area of a quadrant of the unit circle is Pi/4 and the area of the unit circle is Pi. What are these 2 sectors and why the relationship between the 2? https://en.wikipedia.org/wiki/Circular_sector When sin*cosin=1/4 then area of the one sector is Pi/24 and area of second sector is 5Pi/24 Link to comment Share on other sites More sharing options...
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