Answer:
[tex]\frac{11}{12}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1, then
cosx = [tex]\sqrt{1-sin^2x}[/tex]
note that ([tex]\frac{\sqrt{23} }{12}[/tex] )² = [tex]\frac{23}{144}[/tex]
cosΘ = [tex]\sqrt{1-\frac{23}{144} }[/tex] = [tex]\sqrt{\frac{121}{144} }[/tex] = [tex]\frac{11}{12}[/tex]
