SOLUTION: Find sin(x/2), cos(x/2), and tan(x/2) from the given information tan(x)=1; 0 degrees< x <90 degrees

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Question 1056788: Find sin(x/2), cos(x/2), and tan(x/2) from the given information
tan(x)=1; 0 degrees< x <90 degrees
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
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Find sin(x/2), cos(x/2), and tan(x/2) from the given information
tan(x)=1; 0 degrees< x <90 degrees
~~~~~~~~~~~~~~~~~~~~~~~~~ 

The condition "tan(x)=1; 0° < x < 90° " implies

x = 45°.


Then x/2 = 22°30'.


To calculate  sin(22°30'), apply the formula of half argument for sines  (see the lesson  Trigonometric functions of half argument in this site):

sin(22°30') =  =  =  = .



Similarly, 

cos(22°30') =  =  =  = .


Hence,

tan(22°30') = sin(22°30')/cos(22°30') =  =  =  =  = .

See the lesson  Trigonometric functions of half argument - Examples in this site.


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