SOLUTION: use a half angle identity to find the exact value of the expression sin 105 degrees

Algebra.Com
Question 482089: use a half angle identity to find the exact value of the expression
sin 105 degrees

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
use a half angle identity to find the exact value of the expression
sin 105 degrees.
**
sin(x/2)=±√((1-cosx)/2)
sin 105º=sin (210º/2)=±√((1-cos210º)/2)
cos 210º=cos 30º=-√3/2 (in quadrant III where cos<0)
=±√((1+√3/2)/2)
multiply by LCD 2
=±√((2+√3)/4)
take sqrt of positive root because sin 105º in quadrant II is positive
sin 105º=√(2+√3)/2

RELATED QUESTIONS

Use a half-angle identity to find the exact value of the expression. sin 112.5... (answered by robertb)
How would I use a half-angle identity to find the exact value of sin 75... (answered by lwsshak3)
θ=157.5° Use a half-angle identity to find the exact value of... (answered by stanbon)
Use a half - angle identity to find the exact value of each expression. 5) tan 45° (answered by ikleyn,MathLover1)
Use a double- or half-angle identity to find the exact value of each trigonometric... (answered by lwsshak3)
Use half-angle identity to find the exact value of... (answered by solver91311)
Use a half-angle identity to find the exact value of this expression. Given... (answered by Edwin McCravy)
Use half-angle identity to find the exact value of tan 22.5... (answered by lwsshak3)
Use a half angle identity to find the exact value of sin(pi/12) Show work... (answered by stanbon)