Trigonometric functions are applicable to the right-angled triangles. The value of the Sin(Y), Cos(Y), and Tan(Y) are 0.976, 0.219 and 4.445.
What are Trigonometric functions?
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
Given to us
XY = 41
YZ = 9
XZ = 40
In ΔXYZ for ∠Y,
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\rm Sin (\angle Y)=\dfrac{XZ}{XY}\\\\\rm Sin (\angle Y)=\dfrac{40}{41}\\\\[/tex]
[tex]\rm Cos \theta=\dfrac{Base}{Hypotenuse}\\\\ Cos (\angle Y)=\dfrac{ZY}{XY}\\\\ Cos (\angle Y)=\dfrac{9}{41}[/tex]
[tex]\rm Tan \theta=\dfrac{Perpendicular}{Base}\\\\Tan \theta=\dfrac{XZ}{ZY}\\\\Tan \theta=\dfrac{40}{9}[/tex]
Hence, the value of the Sin(Y), Cos(Y), and Tan(Y) are 0.976, 0.219 and 4.445.
Learn more about Trigonometric functions:
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