Question

Consider △XYZ

Triangle X Y Z is shown. Angle X Z Y is a right angle.

What are the ratios of sine, cosine, and tangent for angle Y?

sin(Y) = StartFraction X Z Over X Y EndFraction; cos(Y) = StartFraction Y Z Over X Z EndFraction; tan(Y) = StartFraction Y Z Over X Y EndFraction
sin(Y) = StartFraction X Y Over X Z EndFraction; cos(Y) = StartFraction X Z Over X Y EndFraction; tan(Y) = StartFraction Y Z Over X Z EndFraction
sin(Y) = StartFraction X Z Over X Y EndFraction; cos(Y) = StartFraction Y Z Over X Y EndFraction; tan(Y) = StartFraction X Z Over Y Z EndFraction
sin(Y) = StartFraction Y Z Over X Y EndFraction; cos(Y) = StartFraction X Z Over X Y EndFraction; tan(Y) = StartFraction X Z Over Y Z EndFraction

Answer 1

Correct ratios: sin(Y) = XZ/XY, cos(Y) = YZ/XY, tan(Y) = XZ/YZ.

Explanation: Z is the right angle so hypotenuse = XY. For angle Y, opposite side = XZ and adjacent = YZ, giving sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.