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

Answer:

For angle Y

$sin = \frac{xy}{xz}$

$cos = \frac{yz}{xz}$

Answer 2

The ratios of sine, cosine, and tangent for angle Y are

sin(Y) = XZ/XY; cos(Y) = ZY/XY; tan(Y) = XZ/ZY.

Given:

XYZ is a right-angled triangle  

In ΔXYZ, ∠XZY is the right angle

To find:

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

Solution:

Formula used:

From trigonometric ratios

sine = Opposite side/Hypotenuse

cosine = Adjacent side/Hypotenuse

tangent = Opposite side/Adjacent side

Here we have

XYZ is a right-angled triangle  

In ΔXYZ, ∠XZY is the right angle  

From ∠Y in ΔXYZ,

Opposite side = XZ

Adjacent side = ZY

Hypotenuse = XY

[ For more understanding observe the given picture ]

By the given formulas,

sin(Y) = Opposite side/Hypotenuse = XZ/XY

cos(Y) = Adjacent side/Hypotenuse = ZY/XY

tan(Y) = Opposite side/Adjacent side = XZ/ZY  

Therefore,

The ratios of sine, cosine, and tangent for angle Y are

sin(Y) = XZ/XY; cos(Y) = ZY/XY; tan(Y) = XZ/ZY.  

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