Converting degree into variable 'x'

[L²Cc]

Homework Statement

After integrating x²/(sqrt1-x²) using the triangle method and thereby substituting sin¤ for x, I ended up with the result 1/2¤-1/2sin2¤+c. For my answer toge complete, I must have the ¤ in x format. I managed to convert the 1/2¤, which is simply 1/2arcsinx but I couldn't for 1/2sin2¤, my answer did not agree with the textbook's which read 1/2x(sqrt1-x²)...

My computer won't read latex at the moment so please excuse the amateur notation. Thank you.

Homework Equations

I think I covered it all above!

 

[qspeechc]

sin2x = 2sinx.cosx

 

[Architeuthis Dux]

The solution to this problem involves understanding the properties of trigonometric functions and their relationship to degrees and radians. In this case, the variable x represents the sine of an angle, which can be expressed in degrees or radians. To convert degrees into a variable, you can use the fact that 1 degree is equal to π/180 radians. So, to convert 1/2sin2¤ into a variable, you can use the substitution x=sin¤ and then use the conversion factor to write it as x=(π/180)¤. This will give you the final answer of 1/2x(sqrt1-x²), which agrees with the textbook's answer. It is important to understand the relationship between degrees and radians in order to accurately convert between them and solve problems involving trigonometric functions.